Martyn Waghorn hit a hat-trick as Rangers crushed Cowdenbeath to move into the Scottish Cup fifth round.
Lee Wallace and Barrie McKay put the Championship leaders two goals ahead just after the half-hour mark.
A terrific Dean Brett free-kick gave the League One side a modicum of hope just before half-time.
Before the hour mark Waghorn scored twice, the second from the penalty spot, and another penalty 12 minutes from the end completed the demolition.
The prolific striker has now scored 25 goals in 27 games for the club he joined in the summer, more than any other player in the top four divisions this season.
Cowdenbeath, sitting seventh in League One, were 18-1 underdogs coming to Ibrox and any notion of an upset was extinguished early.
It might have taken Rangers 19 minutes to open the scoring, Kenny Miller playing in Wallace who put his shot through Jamie Sneddon's legs, but the home team's dominance was obvious long before then.
At times, it was akin to a training session instead of a cup tie. The forwards-versus-defence vibe carried on for the vast part of the day. When McKay drove at the Cowdenbeath defence, who conveniently backed off him, and slammed home Rangers' second, the game was done.
There was respite for Cowdenbeath but, though beautiful, it was all too brief. Brett's free-kick was perfectly executed, up and over the wall and into the net via the underside of Wes Foderingham's crossbar.
At 2-1, the game was, in theory, alive but the reality was Rangers had extra gears and they did not take long in finding them. Miller had a shot hoofed off the line at the beginning of the second half, then Waghorn had an effort tipped away by Sneddon.
Rangers had upped the pace and the goals soon came. A nice flick from Gedion Zelalem, some good strength from Waghorn and weak defending from Cowdenbeath saw the striker thump home the third three minutes into the new half.
Seven minutes after that, Fraser Kerr took out James Tavernier in the box and Waghorn put away the penalty.
Just after the hour, Rangers boss Mark Warburton made some changes and on came Harry Forrester for his debut following his move from Doncaster. As far as pleasant introductions go, this was as cushy as they come.
Rangers got their fifth when Tavernier went down under a challenge from Chris Kane. It was the hat-trick goal for Waghorn on a day when the Ibrox club barely had to break sweat to make Monday's draw for the fifth round.
Full Time Match ends, Rangers 5, Cowdenbeath 1.
90:00 +2:09 Full timeFull Time Second Half ends, Rangers 5, Cowdenbeath 1.
90:00 +0:37Attempt saved. Dean Shiels (Rangers) right footed shot from outside the box is saved in the centre of the goal.
90:00 +0:14Corner, Rangers. Conceded by Brad Donaldson.
89:47Corner, Rangers. Conceded by Ali El-Zubaidi.
88:49Attempt missed. Harry Forrester (Rangers) right footed shot from outside the box is just a bit too high.
86:12Attempt missed. Harry Forrester (Rangers) right footed shot from outside the box is close, but misses to the left.
85:27Attempt missed. James Tavernier (Rangers) right footed shot from the centre of the box misses to the left.
83:50 BookingBooking Ali El-Zubaidi (Cowdenbeath) is shown the yellow card.
83:17Harry Forrester (Rangers) wins a free kick in the attacking half.
83:17Foul by Brad Donaldson (Cowdenbeath).
80:22Martyn Waghorn (Rangers) wins a free kick in the attacking half.
80:22Foul by Ali El-Zubaidi (Cowdenbeath).
79:25Foul by Dean Shiels (Rangers).
79:25Brad Donaldson (Cowdenbeath) wins a free kick on the right wing.
78:41 SubstitutionSubstitution Substitution, Cowdenbeath. Ali El-Zubaidi replaces Declan Hughes.
77:59 Goal scoredGoal! Goal! Rangers 5, Cowdenbeath 1. Martyn Waghorn (Rangers) converts the penalty with a left footed shot to the bottom left corner.
77:59 BookingBooking Dean Brett (Cowdenbeath) is shown the yellow card.
77:15Penalty Rangers. James Tavernier draws a foul in the penalty area.
77:15Penalty conceded by Chris Kane (Cowdenbeath) after a foul in the penalty area.
Substitution Substitution, Cowdenbeath. Craig Johnston replaces Gordon Smith.
70:47 SubstitutionSubstitution Substitution, Rangers. Ryan Hardie replaces Kenny Miller.
67:55Attempt blocked. Barrie McKay (Rangers) right footed shot from outside the box is blocked.
64:44Harry Forrester (Rangers) wins a free kick on the left wing.
64:44Foul by Dean Brett (Cowdenbeath).
61:44 SubstitutionSubstitution Substitution, Rangers. Harry Forrester replaces Gedion Zelalem.
61:33 SubstitutionSubstitution Substitution, Rangers. Dean Shiels replaces Andy Halliday.
61:18Attempt missed. Greig Spence (Cowdenbeath) right footed shot from outside the box is just a bit too high.
60:31Lee Wallace (Rangers) wins a free kick on the right wing.
60:31Foul by Brad Donaldson (Cowdenbeath).
59:00Attempt saved. Martyn Waghorn (Rangers) left footed shot from the right side of the box is saved in the centre of the goal.
58:42Corner, Rangers. Conceded by Pat Scullion.
57:59Corner, Rangers. Conceded by Brad Donaldson.
57:30Corner, Rangers. Conceded by Chris Kane.
57:24Attempt blocked. Barrie McKay (Rangers) right footed shot from outside the box is blocked.
55:42 SubstitutionSubstitution Substitution, Cowdenbeath. Chris Kane replaces Lewis Milne.
54:55 Goal scoredGoal! Goal! Rangers 4, Cowdenbeath 1. Martyn Waghorn (Rangers) converts the penalty with a left footed shot to the bottom left corner.
54:23Penalty Rangers. James Tavernier draws a foul in the penalty area.
54:23Penalty conceded by Fraser Kerr (Cowdenbeath) after a foul in the penalty area.
54:00Lee Wallace (Rangers) wins a free kick on the left wing.
53:58Foul by Dean Brett (Cowdenbeath).
53:34Attempt saved. Gedion Zelalem (Rangers) right footed shot from the centre of the box is saved in the bottom right corner.
52:57Attempt missed. Kenny Miller (Rangers) right footed shot from the left side of the box is just a bit too high.
51:56Attempt saved. Jason Holt (Rangers) right footed shot from outside the box is saved in the top centre of the goal.
51:11Attempt missed. Kenny Adamson (Cowdenbeath) right footed shot from outside the box is high and wide to the left.
50:03Attempt missed. Liam Callaghan (Cowdenbeath) right footed shot from the right side of the box is close, but misses the top left corner.
49:41Corner, Cowdenbeath. Conceded by Danny Wilson.
48:31Foul by Gedion Zelalem (Rangers).
48:31Liam Callaghan (Cowdenbeath) wins a free kick on the right wing.
47:38 Goal scoredGoal! Goal! Rangers 3, Cowdenbeath 1. Martyn Waghorn (Rangers) left footed shot from the centre of the box to the high centre of the goal. Assisted by Gedion Zelalem.
46:32Corner, Rangers. Conceded by Jamie Sneddon.
46:25Attempt saved. Martyn Waghorn (Rangers) left footed shot from outside the box is saved in the centre of the goal.
45:54Attempt saved. Kenny Miller (Rangers) right footed shot from very close range is saved in the bottom left corner.
45:00Second Half begins Rangers 2, Cowdenbeath 1.
45:00 +0:07 Half timeHalf Time First Half ends, Rangers 2, Cowdenbeath 1.
44:23Corner, Rangers. Conceded by Lewis Milne.
44:18Attempt blocked. Jason Holt (Rangers) right footed shot from outside the box is blocked.
43:33Attempt missed. Martyn Waghorn (Rangers) left footed shot from the centre of the box is close, but misses to the left.
42:30Martyn Waghorn (Rangers) wins a free kick in the attacking half.
42:30Foul by Lewis Milne (Cowdenbeath).
41:43Attempt missed. Lee Wallace (Rangers) right footed shot from the centre of the box is high and wide to the right.
39:58 Goal scoredGoal! Goal! Rangers 2, Cowdenbeath 1. Dean Brett (Cowdenbeath) from a free kick with a right footed shot to the top right corner.
39:00Foul by Dominic Ball (Rangers).
39:00Greig Spence (Cowdenbeath) wins a free kick in the defensive half.
35:39Corner, Rangers. Conceded by Pat Scullion.
32:46 Goal scoredGoal! Goal! Rangers 2, Cowdenbeath 0. Barrie McKay (Rangers) right footed shot from outside the box to the bottom right corner. Assisted by Martyn Waghorn.
28:48Corner, Rangers. Conceded by Pat Scullion.
28:41Attempt blocked. Gedion Zelalem (Rangers) right footed shot from the centre of the box is blocked.
27:16Attempt saved. Lee Wallace (Rangers) right footed shot from the centre of the box is saved in the centre of the goal.
20:53Corner, Cowdenbeath. Conceded by James Tavernier.
20:15Attempt saved. James Tavernier (Rangers) right footed shot from outside the box is saved in the centre of the goal.
19:44Corner, Rangers. Conceded by Kenny Adamson.
18:20 Goal scoredGoal! Goal! Rangers 1, Cowdenbeath 0. Lee Wallace (Rangers) left footed shot from the centre of the box to the centre of the goal. Assisted by Kenny Miller.
18:06Attempt blocked. Andy Halliday (Rangers) right footed shot from outside the box is blocked.
17:46 BookingBooking Declan Hughes (Cowdenbeath) is shown the yellow card for a bad foul.
17:42Foul by Declan Hughes (Cowdenbeath).
17:42Lee Wallace (Rangers) wins a free kick in the attacking half.
15:21Attempt missed. Martyn Waghorn (Rangers) right footed shot from outside the box is close, but misses the top left corner.
10:38Corner, Rangers. Conceded by Liam Callaghan.
9:11Attempt missed. Martyn Waghorn (Rangers) right footed shot from outside the box is just a bit too high.
8:26Attempt saved. Kenny Miller (Rangers) left footed shot from the left side of the box is saved in the centre of the goal.
7:21Attempt missed. Greig Spence (Cowdenbeath) header from the centre of the box is close, but misses to the left.
5:52Foul by Dominic Ball (Rangers).
5:52Declan Hughes (Cowdenbeath) wins a free kick in the attacking half.
5:00Foul by Danny Wilson (Rangers).
5:00Gordon Smith (Cowdenbeath) wins a free kick in the attacking half.
4:40Attempt missed. Martyn Waghorn (Rangers) right footed shot from the left side of the box is just a bit too high.
3:49Corner, Rangers. Conceded by Declan Hughes.
3:45Attempt blocked. Lee Wallace (Rangers) right footed shot from outside the box is blocked.
2:32Attempt missed. James Tavernier (Rangers) right footed shot from outside the box is just a bit too high.
1:04Andy Halliday (Rangers) wins a free kick in the attacking half.
1:04Foul by Gordon Smith (Cowdenbeath).
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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