David Silva was at the heart of the champions’ best work and he must have thought he had helped his side to all three points when his deflected shot was headed home by Fernandinho to break the deadlock with just over 15 minutes remaining.
But Roberto Martinez’s side roared back minutes later as Steven Naismith rose highest to head Leighton Baines’ brilliant free-kick past Joe Hart and into the bottom corner for a share of the spoils.
Manchester City, who were without Yaya Toure due to his Africa Cup of Nations commitments, had not won an away match without the Ivory Coast midfielder since January 2013 and were looking to end that run on Merseyside.
Pellegrini was looking for someone to fill the powerful Ivorian’s void at Goodison Park and Silva stepped into the mantle beautifully in the opening minutes, skipping past the tackle of Muhamed Besic before releasing Jesus Navas down the right, but the Spaniard’s cross was well blocked.
Silva was a constant menace to the home defence and he pounced on the ball after Seamus Coleman was robbed in the middle of the park and drove forward, releasing Stevan Jovetic into space but the striker dragged his shot wide.
The Spaniard again picked up the ball following Phil Jagielka’s mistake and played Navas through on goal but the shot was pulled wide without testing Joel in the Everton goal.
With the home crowd growing restless Everton suddenly burst into life as Romelu Lukaku went through on goal, but Hart, who was quiet for large parts of the first 45 minutes, produced an important save from the Belgian striker’s angled shot.
Seconds later the ball found its way to the feet of Coleman and the full-back’s shot beat Hart all ends up but cannoned back off the crossbar.
Martinez would have wanted more of the same after the break and they produced the first chance of the second half as Ross Barkley fired a free-kick over the wall but it failed to hit the target.
Everton looked dangerous when they could get service to Lukaku and he caused Eliaquim Mangala plenty of problems as he tried to wrestle down the right touchline, but the French defender hauled him back and was shown a yellow card.
Minutes later, Lukaku breezed past Mangala again but his left foot shot across goal was once again well saved by Hart.
With City looking to keep pace with leaders Chelsea, Pellegrini sent on Sergio Aguero with just over 20 minutes left but it was Everton who thought they had taken the lead.
Jagielka poked the ball into the back of the net from close range after Hart fumbled Baines testing free-kick, but referee Martin Atkinson decided Naismith had fouled the England goalkeeper.
City were still frantically searching for a winner when the ball bounced into the path of Aguero on the edge of the box, but the Argentine, perhaps lacking sharpness after his injury lay-off, screwed his shot wide.
But City persevered and they finally got their reward when Silva’s deflected shot fell into the path of Fernandinho and the Brazilian headed past Joel from close range to give his side the lead.
Pellegrini could have been forgiven for thinking his side were home and dry but Everton had other ideas and they bounced straight back thanks to Naismith’s powerful header from Baines’ free-kick.
The visitors introduced Frank Lampard late in the day but apart from a half-chance for Samir Nasri, Everton were not to be denied their much-deserved point, which takes them up to 12th in the table.
City, who are now unbeaten in 12 Premier League matches, find themselves two points adrift of Chelsea at the top of the Premier League.
Soccer Saturday analysis – Charlie Nicholas
I thought Man City and, in particular Silva, were a constant threat all day, but you expect that with the quality that the little genius has got. Everton reverted back to their old system with Barkley just behind Lukaku and it didn’t suit Barkley as much – but it suited Lukaku better and he had the pace to take on both centre-backs of Man City. The second half was great. With a strong wind blowing it was hard to get perfect passing and both teams tried their best. When Man City got the goal I thought the game would be over, but when Everton equalised it was end-to-end with both teams at full pelt trying to get three points. I thoroughly enjoyed it.
Everton: Joel (7), Coleman (7), Jagielka (6), Stones (8), Baines (7), Besic (6), Barry (6), McGeady (6), Naismith (8), Barkley (7), Lukaku (7).
Subs used: Mirallas (6).
Man City: Hart (7), Zabaleta (7), Demichelis (6), Mangala (5), Clichy (6), Fernando (6), Fernandinho (7), Navas (7), Silva (8), Nasri (7), Jovetic (6).
Subs used: Kolarov (5), Aguero (5), Lampard (5).
Man of the Match: David Silva