Manchester City continued their unbeaten start to the Premier League season but had to settle for a point against a battling Everton side.
Everton scored when Marouane Fellaini turned in Leighton Baines's cross after Joe Hart saved his initial header.
Carlos Tevez levelled from the spot after Fellaini dragged down Edin Dzeko.
City had the better of a tight second half but struggled to create chances and Everton almost snatched victory with Nikica Jelavic's free-kick.
Moyes's record against Mancini
01 Dec 2012 Man City 1-1 Everton
31 Jan 2012 Everton 1-0 Man City
24 Sep 2011 Man City 2-0 Everton
7 May 2011 Everton 2-1 Man City
20 Dec 2010 Man City 1-2 Everton
23 Mar 2010 Man City 0-2 Everton
16 Jan 2010 Everton 2-0 Man City
The draw was enough to send Roberto Mancini's side to the top of the table on goal difference, at least until Manchester United play Reading in Saturday's late game.
It will still be viewed as two points dropped in the title race, especially as City had won 29 of their last 31 home league games ahead of the visit of the Toffees.
But David Moyes' fine record against Mancini, who has now only won only one of seven meetings with Everton, always suggested things would not be straightforward for the champions.
Both sides began cautiously, with the game getting bogged down in a midfield battle until Everton took the lead just after the half hour mark.
Vincent Kompany could only flick on a whipped Leighton Baines cross and, although Hart kept out Fellaini's initial header with a fine reflex save, he was helpless to stop the Belgian bundling the rebound in with his thigh.
City responded by fashioning their first real chances of the game, with Tim Howard clawing away a Tevez header and then turning Dzeko's snap-shot around his post.
The corner that followed saw Fellaini concede the controversial penalty that led to City's equaliser, with Dzeko going to ground after having his shirt tugged by the Belgian.
Referee Lee Probert pointed to the spot and Tevez stepped up to fire down the centre of the goal.
Everton still ended the half on the attack, with Fellaini forcing a sprawling save from Hart just before the interval, but the Toffees were firmly on the backfoot afterwards.
Only frustration was to follow for City, however. They dominated possession but could find no way through Everton's determined defence and their only effort on goal saw Howard push away Maicon's swerving shot.
The home fans could not understand Mancini's decision to replace the hard-working Tevez with Sergio Aguero as he juggled his attack.
In truth, the Argentine's introduction, as well as that of Mario Balotelli, had little impact - Everton were just too well organised at the back.
A difficult afternoon for City could have been worse - Hart had to readjust when Jelavic's free-kick bounced in front of him, and he only just managed to push the ball around his post.
But a draw - Everton's seventh in their last nine games - was probably the fairest result.
Manchester City boss Roberto Mancini: "Everton is always a difficult game because they work hard, they defend very well.
"In the second half we played better, probably deserved to score another goal.
"In the end we are not happy but the season is long and this doesn't change anything.
"If you don't pay attention you can lose three points and it is sometimes better to take one."
Everton manager David Moyes on Manchester City's equaliser: "It is not a penalty kick.
"You can't be giving ones like that. There'd be a penalty every time there's a corner kick.
"The fourth official told me that it was given for a foul by Leon Osman, so I've got my doubts if the referee saw the incident. But even if it was Fellaini, it's not a penalty kick, nowhere near.
"They say it levels itself out. We'll see."
Live Text Commentary
Full Time The match has reached full-time.90:00 +2:29
Samir Nasri sends in a cross, Sylvain Distin manages to make a clearance.90:00 +2:00
Free kick awarded for an unfair challenge on Vincent Kompany by Marouane Fellaini. Direct free kick taken by Yaya Toure.90:00 +1:05
Tim Howard restarts play with the free kick.90:00 +1:05 Substitution
Substitution Johnny Heitinga is brought on as a substitute for Nikica Jelavic.90:00 +1:05
Mario Balotelli is penalised for a handball.90:00 +0:08
Leon Osman concedes a free kick for a foul on Mario Balotelli. Yaya Toure restarts play with the free kick.87:51
Nikica Jelavic has a direct shot on goal from the free kick, save by Joe Hart. Steven Pienaar takes a inswinging corner from the left by-line to the near post, Mario Balotelli makes a clearance.87:51 Booking
Booking Pablo Zabaleta receives a caution.87:45
Unfair challenge on Nikica Jelavic by Pablo Zabaleta results in a free kick.86:21
Inswinging corner taken from the left by-line by Samir Nasri, clearance made by Leon Osman.85:05
Free kick awarded for an unfair challenge on Phil Jagielka by Mario Balotelli. Tim Howard restarts play with the free kick.84:14
Mario Balotelli has an effort at goal from outside the penalty box which goes wide right of the target.83:58
Samir Nasri fouled by Nikica Jelavic, the ref awards a free kick. Yaya Toure takes the free kick.82:22
Free kick awarded for an unfair challenge on Joleon Lescott by Nikica Jelavic. Free kick taken by Yaya Toure.81:49
The ball is sent over by Mario Balotelli, Tony Hibbert manages to make a clearance.79:47 Substitution
Substitution Edin Dzeko goes off and Mario Balotelli comes on.77:04
Free kick awarded for an unfair challenge on Leon Osman by Gareth Barry. Free kick taken by Phil Jagielka.76:21
Gareth Barry gives away a free kick for an unfair challenge on Bryan Oviedo. Sylvain Distin takes the direct free kick.74:47
Bryan Oviedo produces a cross.
Free kick awarded for an unfair challenge on Leon Osman by Sergio Aguero. Free kick taken by Leighton Baines.72:37 Substitution
Substitution Bryan Oviedo joins the action as a substitute, replacing Steven Naismith.71:56
Corner taken left-footed by Leighton Baines to the near post, Pablo Zabaleta makes a clearance.70:57
Foul by Vincent Kompany on Nikica Jelavic, free kick awarded. Direct free kick taken by Leighton Baines.69:54
Steven Naismith fouled by David Silva, the ref awards a free kick. Tim Howard takes the free kick.68:55
Direct free kick taken by Joleon Lescott.68:55 Booking
Booking Marouane Fellaini booked for unsporting behaviour.68:32
Foul by Marouane Fellaini on Pablo Zabaleta, free kick awarded.67:14 Substitution
Substitution Sergio Aguero on for Carlos Tevez.67:14
A cross is delivered by Darron Gibson.66:22
Darron Gibson takes a shot. Joleon Lescott gets a block in.64:09
Samir Nasri takes a inswinging corner from the left by-line played to the near post.62:14
Sisenando Maicon takes a shot. Tim Howard makes a save.59:20
Headed effort from deep inside the penalty area by Carlos Tevez misses to the left of the goal.57:11
Phil Jagielka challenges Edin Dzeko unfairly and gives away a free kick. Free kick taken by Pablo Zabaleta.56:52
Steven Naismith produces a cross, save by Joe Hart.56:24
Handball decision goes against Sisenando Maicon. Darron Gibson takes the direct free kick.56:00
Yaya Toure challenges Marouane Fellaini unfairly and gives away a free kick. Sylvain Distin restarts play with the free kick.54:25
Free kick awarded for a foul by Vincent Kompany on Nikica Jelavic. Free kick taken by Leighton Baines.54:09
Pablo Zabaleta sends in a cross.53:53
Edin Dzeko takes a shot. Phil Jagielka gets a block in.52:12
The ball is crossed by Pablo Zabaleta.51:03
Darron Gibson produces a right-footed shot from outside the box and misses left.48:23
Free kick awarded for a foul by Marouane Fellaini on Gareth Barry. Samir Nasri restarts play with the free kick.47:26
Carlos Tevez takes a shot. Blocked by Phil Jagielka.46:38
Free kick awarded for a foul by Carlos Tevez on Leon Osman. Direct free kick taken by Tim Howard.45:01
The referee blows his whistle to start the second half.45:00 +2:36 Half time
Half Time The players leave the pitch at half time.45:00 +1:58
Steven Pienaar sends in a cross, Marouane Fellaini takes a shot. Joe Hart makes a save.45:00 +1:24
Leighton Baines restarts play with the free kick.45:00 +1:24 Booking
Booking Joleon Lescott booked for unsporting behaviour.45:00 +1:11
Free kick awarded for an unfair challenge on Steven Pienaar by Joleon Lescott.45:00 +0:20
Sylvain Distin fouled by Edin Dzeko, the ref awards a free kick. Tim Howard takes the direct free kick.44:23
Corner from the right by-line taken by David Silva, Nikica Jelavic manages to make a clearance.42:49
The assist for the goal came from Edin Dzeko.42:49 Goal scored
Goal! - Carlos Tevez - Man City 1 - 1 Everton Penalty taken right-footed by Carlos Tevez and scored. Man City 1-1 Everton.41:24
Edin Dzeko takes a shot. Save by Tim Howard. Corner from the left by-line taken by Samir Nasri, Unfair challenge on Edin Dzeko by Marouane Fellaini results in a Penalty.39:21
Steven Pienaar fouled by Yaya Toure, the ref awards a free kick. Direct free kick taken by Sylvain Distin.37:40
Carlos Tevez takes a shot. Blocked by Leighton Baines.36:09
Carlos Tevez takes a shot. Save by Tim Howard. Corner from the right by-line taken by David Silva, Leon Osman makes a clearance.34:28
Carlos Tevez concedes a free kick for a foul on Leon Osman. Sylvain Distin restarts play with the free kick.32:24
Assist by Leighton Baines.32:24 Goal scored
Goal! - Marouane Fellaini - Man City 0 - 1 Everton Marouane Fellaini fires in a goal from inside the six-yard box high into the middle of the goal. Man City 0-1 Everton.32:16
Marouane Fellaini takes a shot. Save by Joe Hart.31:39
Foul by Yaya Toure on Marouane Fellaini, free kick awarded. Phil Jagielka restarts play with the free kick.29:12
Free kick awarded for a foul by Vincent Kompany on Nikica Jelavic. Leighton Baines restarts play with the free kick.27:10
The referee blows for offside against Gareth Barry. Free kick taken by Tim Howard.24:55
The ball is delivered by Leighton Baines.23:45
Samir Nasri takes a shot.20:07
A cross is delivered by David Silva, Sylvain Distin makes a clearance.19:01
Foul by Steven Pienaar on Sisenando Maicon, free kick awarded. Direct free kick taken by David Silva.17:56
Edin Dzeko fouled by Sylvain Distin, the ref awards a free kick. Direct free kick taken by Sisenando Maicon.12:29
Unfair challenge on Pablo Zabaleta by Steven Naismith results in a free kick. Joe Hart takes the direct free kick.8:32
The ball is swung over by Sisenando Maicon, save made by Tim Howard.6:43 Substitution
Substitution Pablo Zabaleta replaces Aleksandar Kolarov.6:27
Shot from outside the penalty box by Leon Osman goes wide right of the goal.3:17
Steven Naismith has an effort at goal from just outside the penalty box which goes wide of the left-hand post.1:51
Unfair challenge on Yaya Toure by Leighton Baines results in a free kick. Joe Hart restarts play with the free kick.0:00
The referee gets the game started.
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