Norwich produced a battling second half display to hold Everton to their third straight Premier League draw.
Toffees striker Romelu Lukaku scored for the sixth successive league game with a header from Gerard Deulofeu's excellent cross.
Leighton Baines was denied by the woodwork, while Arouna Kone and Lukaku also missed chances for Everton.
Wes Hoolahan levelled for Norwich from close range before Cameron Jerome missed a great chance for the hosts.
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All the action and reaction from Saturday's Premier League games
Lukaku now has 15 league and cup goals this season, seven in his last six league games and is second in the Premier League's top scorers with 12 behind Leicester's Jamie Vardy (14).
His header from Deulofeu's floated delivery displayed everything that is good about the Belgium striker.
But Lukaku went on to spurn a host of chances as Everton failed to add to their early lead despite dominating a Norwich side that looked desperately short of confidence before the interval.
Baines was denied a goal on his first league start of the season while Kone was also guilty of wasting a couple of chances before Norwich came back strongly after the break.
While Everton remain unbeaten in six league games, improvements are required if they are to seriously push for a European place.
Norwich, who conceded early on, went into the match with just one clean sheet in 15 league games.
But Everton's failure to extend their lead allowed the hosts a point that looked beyond them during a one-sided first half.
Neil responded at the start of the second half by replacing Andre Wisdom with Ryan Bennett and it was a change that produced an instant response as Hoolahan bundled Bennett's header over the line.
Norwich went for the winner in this entertaining match but their finishing was as bad as Everton's - Jerome somehow squandering an excellent chance from eight yards.
Norwich manager Alex Neil: "If we perform like we did in the second half then we will be fine.
"We had a good discussion in terms of what's acceptable and all the questions I posed to them at half-time they came out and answered.
"Tactically nothing changed. All that changed in the second half was the way we went about our business."
Everton manager Roberto Martinez: "Football can be cruel at times and it was today. There is considerable frustration when you create so many chances and you don't get the second goal.
"You end up having something to lose. Norwich could have been out of the game at half-time but we gave them a little bit of hope.
"Then the belief and momentum goes into them with the goal."
Norwich now face back-to-back away games at Manchester United (19 December) and Tottenham (26 December) before their next Carrow Road appearance.
Martinez and his Everton players have a full week to work on killing teams off before leaders Leicester City visit Goodison Park on 19 December.
Full Time Match ends, Norwich City 1, Everton 1.
90:00 +3:08 Full timeFull Time Second Half ends, Norwich City 1, Everton 1.
90:00 +2:32Attempt blocked. Kevin Mirallas (Everton) right footed shot from the left side of the box is blocked.
90:00 +1:14 BookingBooking Russell Martin (Norwich City) is shown the yellow card for a bad foul.
90:00 +1:11Kevin Mirallas (Everton) wins a free kick in the defensive half.
90:00 +1:11Foul by Russell Martin (Norwich City).
90:00 +0:34Attempt missed. Darron Gibson (Everton) right footed shot from outside the box is too high. Assisted by Kevin Mirallas.
89:45Attempt missed. Jonny Howson (Norwich City) right footed shot from outside the box is just a bit too high. Assisted by Cameron Jerome.
85:58Foul by Arouna Koné (Everton).
85:58Martin Olsson (Norwich City) wins a free kick in the defensive half.
85:04Ramiro Funes Mori (Everton) wins a free kick in the defensive half.
85:04Foul by Cameron Jerome (Norwich City).
84:27Foul by Kevin Mirallas (Everton).
84:27Nathan Redmond (Norwich City) wins a free kick in the defensive half.
83:30 SubstitutionSubstitution Substitution, Norwich City. Jonny Howson replaces Wes Hoolahan.
83:07Attempt missed. Ramiro Funes Mori (Everton) right footed shot from outside the box is too high.
81:28Attempt missed. Gareth Barry (Everton) header from the centre of the box misses to the right. Assisted by Leighton Baines with a cross following a corner.
80:38Corner, Everton. Conceded by Cameron Jerome.
80:03Corner, Everton. Conceded by Russell Martin.
78:16Attempt saved. Gareth Barry (Everton) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Arouna Koné.
Foul by Arouna Koné (Everton).
75:26Wes Hoolahan (Norwich City) wins a free kick in the defensive half.
75:11 SubstitutionSubstitution Substitution, Everton. Darron Gibson replaces Ross Barkley.
74:43Seamus Coleman (Everton) wins a free kick in the defensive half.
74:43Foul by Wes Hoolahan (Norwich City).
72:58Attempt missed. Alexander Tettey (Norwich City) right footed shot from outside the box misses to the right. Assisted by Gary O'Neil.
69:30Attempt missed. Cameron Jerome (Norwich City) right footed shot from the centre of the box is too high. Assisted by Wes Hoolahan.
68:45 SubstitutionSubstitution Substitution, Everton. Kevin Mirallas replaces Gerard Deulofeu.
68:15Attempt missed. Seamus Coleman (Everton) left footed shot from outside the box misses to the right.
68:11Attempt blocked. Arouna Koné (Everton) right footed shot from the centre of the box is blocked. Assisted by Romelu Lukaku.
61:19Tom Cleverley (Everton) wins a free kick in the defensive half.
61:19Foul by Nathan Redmond (Norwich City).
58:17Offside, Norwich City. Wes Hoolahan tries a through ball, but Cameron Jerome is caught offside.
58:14Attempt blocked. Wes Hoolahan (Norwich City) left footed shot from the left side of the six yard box is blocked.
57:03Corner, Norwich City. Conceded by Ramiro Funes Mori.
57:02Attempt blocked. Robbie Brady (Norwich City) right footed shot from outside the box is blocked. Assisted by Wes Hoolahan.
55:16Corner, Norwich City. Conceded by Seamus Coleman.
49:56Gerard Deulofeu (Everton) wins a free kick on the right wing.
49:56Foul by Martin Olsson (Norwich City).
48:34Attempt missed. Tom Cleverley (Everton) right footed shot from the centre of the box is high and wide to the right.
46:03 Goal scoredGoal! Goal! Norwich City 1, Everton 1. Wes Hoolahan (Norwich City) left footed shot from very close range to the bottom right corner following a corner.
46:02Attempt blocked. Ryan Bennett (Norwich City) header from the centre of the box is blocked. Assisted by Robbie Brady with a cross.
45:29Corner, Norwich City. Conceded by Leighton Baines.
45:00Second Half begins Norwich City 0, Everton 1.
45:00 SubstitutionSubstitution Substitution, Norwich City. Ryan Bennett replaces Andre Wisdom.
45:00 +2:12 Half timeHalf Time First Half ends, Norwich City 0, Everton 1.
45:00 +1:36Attempt missed. Romelu Lukaku (Everton) left footed shot from the centre of the box is close, but misses to the left. Assisted by Ross Barkley following a fast break.
45:00 +0:20Delay over. They are ready to continue.
43:33Delay in match Ross Barkley (Everton) because of an injury.
43:33Delay in match Alexander Tettey (Norwich City) because of an injury.
42:23Corner, Everton. Conceded by Sebastien Bassong.
41:38Romelu Lukaku (Everton) wins a free kick in the attacking half.
41:38Foul by Russell Martin (Norwich City).
40:35Attempt missed. Romelu Lukaku (Everton) left footed shot from outside the box is close, but misses to the right. Assisted by Ross Barkley.
39:23Leighton Baines (Everton) wins a free kick in the defensive half.
39:23Foul by Wes Hoolahan (Norwich City).
38:41Leighton Baines (Everton) hits the right post with a right footed shot from the centre of the box. Assisted by Seamus Coleman with a cross.
35:55Offside, Everton. Gerard Deulofeu tries a through ball, but Seamus Coleman is caught offside.
31:33Corner, Norwich City. Conceded by Ramiro Funes Mori.
30:40Attempt missed. Romelu Lukaku (Everton) right footed shot from the left side of the six yard box is close, but misses the top left corner.
27:29Ramiro Funes Mori (Everton) wins a free kick in the defensive half.
27:29Foul by Nathan Redmond (Norwich City).
20:38Foul by Gerard Deulofeu (Everton).
20:38Martin Olsson (Norwich City) wins a free kick in the defensive half.
18:54Foul by Seamus Coleman (Everton).
18:54Wes Hoolahan (Norwich City) wins a free kick in the defensive half.
18:35Attempt saved. Arouna Koné (Everton) right footed shot from the left side of the box is saved in the bottom right corner. Assisted by Romelu Lukaku with a through ball.
14:48 Goal scoredGoal! Goal! Norwich City 0, Everton 1. Romelu Lukaku (Everton) header from very close range to the high centre of the goal. Assisted by Gerard Deulofeu with a cross following a corner.
13:51Corner, Everton. Conceded by Russell Martin.
11:28Attempt missed. Romelu Lukaku (Everton) left footed shot from the left side of the box misses to the right.
10:16Attempt missed. Alexander Tettey (Norwich City) right footed shot from outside the box is too high. Assisted by Wes Hoolahan.
6:56Attempt missed. Nathan Redmond (Norwich City) right footed shot from the right side of the box is close, but misses the top right corner. Assisted by Gary O'Neil.
3:26Ramiro Funes Mori (Everton) wins a free kick in the defensive half.
3:26Foul by Sebastien Bassong (Norwich City).
2:58Corner, Norwich City. Conceded by John Stones.
2:26Foul by Gerard Deulofeu (Everton).
2:26Sebastien Bassong (Norwich City) 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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