Rangers were reduced to 10 men against Morton but still restored their five-point lead at the Championship summit.
Kenny Miller took advantage of a deflection in the box to poke the visitors in front.
Morton gave a good account of themselves but could not score an equaliser, and Barrie McKay played a neat one-two before doubling the lead.
Andy Halliday was shown a second yellow card for celebrating his side's second goal in front of the Morton fans.
The decision riled Rangers' coaching staff, but the team saw out the win against a spirited Morton side.
From the outset, Morton's play was a blend of energy, vigour and intent.
The plot was to pressurise Rangers players, particularly when they took the ball over the halfway line. Both full-backs were also harried, and James Tavernier had an awkward night trying to cope with the lively and spirited Bobby Barr.
The visitors were never wholly comfortable at Cappielow. Even in possession, their passing lacked the tempo or precision that has underpinned so much of their progress this season.
Morton were well served in midfield by Joe Mckee, up front by Denny Johnstone and Declan McManus and at left-back by the sure-footed Mark Russell, who kept Martyn Waghorn unusually quiet. Yet Rangers still carved out some half chances.
Miller would have been frustrated by the way he skewed a header wide from a central position and from close range. Lee Wallace also sent a shot wide from a good position. It was in keeping with the nature of Rangers' performance that their goal came from a moment of luck.
When Halliday struck a shot from 20 yards out, the ball bounced off the chest of defender Thomas O'Ware and fell to Miller, who prodded it past Derek Gaston, the Morton goalkeeper.
The home side did not lose heart, though, and a driving run and cross by McManus caused some alarm for Rob Kiernan, although he managed to slide across to block out the danger. The home fans appealed for hand ball, but it was his leg that made contact.
Morton raised their tempo after the break, which caused anxiety in the Rangers defence as the game opened up. McManus was alert, shooting wide after Rangers conceded possession then seeing his effort saved by Wes Foderingham after Barr had skinned Tavernier on the left and crossed into the box.
Rangers responded by changing their side, with substitutions seeing McKay move into midfield. He grew in stature, striking the bar then embarking on a driving run, playing a one-two with Miller and expertly clipping a shot beyond Gaston's reach and into the net.
The visitors' celebrations were cut short, though, with Halliday shown a second yellow card for gesturing triumphantly to the Morton fans. That decision infuriated Rangers manager Mark Warburton, who was eventually spoken to by the referee Barry Cook.
The dismissal was a set-back, but the home side saw the game out.
Full Time Match ends, Morton 0, Rangers 2.
90:00 +4:02 Full timeFull Time Second Half ends, Morton 0, Rangers 2.
90:00 +3:05Attempt missed. Declan McManus (Morton) header from the centre of the box is high and wide to the left.
90:00 +1:28Corner, Morton. Conceded by James Tavernier.
90:00 +0:09Attempt missed. Declan McManus (Morton) right footed shot from outside the box misses to the right.
89:51Attempt saved. Barrie McKay (Rangers) right footed shot from the centre of the box is saved in the bottom left corner.
89:35Attempt blocked. Ross Forbes (Morton) right footed shot from outside the box is blocked.
88:13Attempt missed. Martyn Waghorn (Rangers) left footed shot from the right side of the box is just a bit too high.
87:44Corner, Morton. Conceded by Wes Foderingham.
87:02Attempt saved. Declan McManus (Morton) right footed shot from outside the box is saved in the centre of the goal.
86:31Attempt saved. Harry Forrester (Rangers) right footed shot from the left side of the box is saved in the top centre of the goal.
85:18Attempt saved. Ross Forbes (Morton) left footed shot from outside the box is saved in the top centre of the goal.
83:53 SubstitutionSubstitution Substitution, Morton. Jon Scullion replaces Bobby Barr.
83:32Attempt missed. Declan McManus (Morton) right footed shot from outside the box misses to the left.
82:06 BookingBooking Michael Tidser (Morton) is shown the yellow card for a bad foul.
81:53 SubstitutionSubstitution Substitution, Morton. Alex Samuel replaces Denny Johnstone.
81:32Foul by Declan McManus (Morton).
81:32Dean Shiels (Rangers) wins a free kick in the defensive half.
80:38Corner, Morton. Conceded by Dominic Ball.
78:45Attempt saved. Harry Forrester (Rangers) left footed shot from the centre of the box is saved in the top centre of the goal.
Substitution Substitution, Morton. Michael Tidser replaces Stefan McCluskey.
74:25 SubstitutionSubstitution Substitution, Rangers. Dominic Ball replaces Kenny Miller.
73:16Foul by Thomas O'Ware (Morton).
73:16Barrie McKay (Rangers) wins a free kick on the left wing.
72:55Foul by Kenny Miller (Rangers).
72:55Joe McKee (Morton) wins a free kick in the defensive half.
71:27 DismissalDismissal Second yellow card to Andy Halliday (Rangers) for a bad foul.
69:51 Goal scoredGoal! Goal! Morton 0, Rangers 2. Barrie McKay (Rangers) right footed shot from the centre of the box to the top left corner. Assisted by Kenny Miller.
69:16Attempt missed. Thomas O'Ware (Morton) right footed shot from the centre of the box is high and wide to the right.
69:05Foul by Lee Wallace (Rangers).
69:05Stefan McCluskey (Morton) wins a free kick on the right wing.
68:35Barrie McKay (Rangers) hits the bar with a right footed shot from outside the box.
67:23 BookingBooking Andy Halliday (Rangers) is shown the yellow card for a bad foul.
67:18Declan McManus (Morton) wins a free kick on the right wing.
67:18Foul by Andy Halliday (Rangers).
66:23 BookingBooking Danny Wilson (Rangers) is shown the yellow card for a bad foul.
66:18Declan McManus (Morton) wins a free kick on the left wing.
66:18Foul by Danny Wilson (Rangers).
65:15Attempt missed. Kenny Miller (Rangers) right footed shot from the centre of the box misses to the right.
62:22Denny Johnstone (Morton) wins a free kick in the defensive half.
62:22Foul by Rob Kiernan (Rangers).
58:58 SubstitutionSubstitution Substitution, Rangers. Dean Shiels replaces Nicky Law.
57:54 SubstitutionSubstitution Substitution, Rangers. Harry Forrester replaces Gedion Zelalem.
56:27Corner, Morton. Conceded by Gedion Zelalem.
55:25Attempt blocked. Nicky Law (Rangers) right footed shot from the right side of the box is blocked.
54:05Bobby Barr (Morton) wins a free kick on the right wing.
54:05Foul by Nicky Law (Rangers).
53:20Attempt saved. Declan McManus (Morton) right footed shot from the centre of the box is saved in the top centre of the goal.
51:56Attempt blocked. Gedion Zelalem (Rangers) right footed shot from outside the box is blocked.
51:00Declan McManus (Morton) wins a free kick on the right wing.
50:58Foul by Danny Wilson (Rangers).
49:55Attempt missed. Declan McManus (Morton) right footed shot from outside the box is high and wide to the left.
48:10Attempt missed. Lee Wallace (Rangers) left footed shot from the left side of the box is high and wide to the left.
47:33Corner, Rangers. Conceded by Thomas O'Ware.
47:00Martyn Waghorn (Rangers) wins a free kick in the defensive half.
46:53Foul by Thomas O'Ware (Morton).
45:51Attempt missed. Martyn Waghorn (Rangers) left footed shot from the right side of the box is high and wide to the left.
45:00Second Half begins Morton 0, Rangers 1.
45:00 +1:01 Half timeHalf Time First Half ends, Morton 0, Rangers 1.
45:00 +0:52Attempt saved. Andy Halliday (Rangers) left footed shot from outside the box is saved in the top centre of the goal.
45:00 +0:24 BookingBooking James Tavernier (Rangers) is shown the yellow card for a bad foul.
45:00 +0:08Foul by James Tavernier (Rangers).
45:00 +0:08Bobby Barr (Morton) wins a free kick in the defensive half.
44:44Corner, Rangers. Conceded by Mark Russell.
43:28Corner, Rangers. Conceded by Thomas O'Ware.
42:56Attempt blocked. Martyn Waghorn (Rangers) right footed shot from outside the box is blocked.
40:45Attempt missed. Joe McKee (Morton) right footed shot from outside the box is high and wide to the right.
38:51Attempt saved. Gedion Zelalem (Rangers) left footed shot from the centre of the box is saved in the centre of the goal.
38:17Attempt blocked. Nicky Law (Rangers) right footed shot from outside the box is blocked.
27:50Attempt missed. Martyn Waghorn (Rangers) right footed shot from the centre of the box misses to the right.
27:40Corner, Rangers. Conceded by Thomas O'Ware.
25:44 Goal scoredGoal! Goal! Morton 0, Rangers 1. Kenny Miller (Rangers) right footed shot from the centre of the box to the bottom right corner.
25:20Attempt blocked. Andy Halliday (Rangers) right footed shot from the centre of the box is blocked.
24:32Corner, Rangers. Conceded by Stefan McCluskey.
23:39Corner, Morton. Conceded by Wes Foderingham.
23:23Attempt saved. Joe McKee (Morton) right footed shot from long range on the left is saved in the bottom right corner.
22:40Foul by Rob Kiernan (Rangers).
22:40Denny Johnstone (Morton) wins a free kick on the left wing.
20:41Hand ball by Conor Pepper (Morton).
20:23Attempt missed. Lee Wallace (Rangers) right footed shot from the left side of the box misses to the left.
19:54Lee Wallace (Rangers) wins a free kick in the attacking half.
19:54Foul by Lee Kilday (Morton).
17:16Foul by Declan McManus (Morton).
17:16Nicky Law (Rangers) wins a free kick on the left wing.
15:49Corner, Morton. Conceded by Rob Kiernan.
8:28Attempt missed. Kenny Miller (Rangers) right footed shot from the centre of the box misses to the right.
6:02Corner, Rangers. Conceded by Conor Pepper.
4:36Corner, Morton. Conceded by James Tavernier.
4:06Foul by Lee Wallace (Rangers).
4:06Stefan McCluskey (Morton) wins a free kick in the defensive half.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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