Fernandinho's second-minute strike was cancelled out by a second-half brace from Connor Wickham, before Samir Nasri earned a late draw for the hosts.
City made their presence felt from the off and when Lee Cattermole was caught in possession, the hosts pounced to take advantage.
Sergio Aguero raced to the edge of the Sunderland box, before a sliding a ball into the path of Fernandinho, who fired into the roof of Vito Mannone's goal.
Sunderland captain John O'Shea spurned two headed chances and Fabio Borini shot wide of the target having found space in the City box as the visitors failed to seize their opportunities to draw level.
Despite City dominating possession throughout the second half, it was Sunderland who snatched the second goal.
Emanuele Giaccherini broke down the left before beating Joe Hart with his cross, leaving Wickham to tap home from close range.
Wickham doubled his tally soon after following a quick break from Borini, which left the Sunderland striker to fire to the right of Hart.
City responded with desperation and earned a point when Nasri's shot from inside the box was pushed into the corner of his own goal by a flailing Mannone.
After playing their part to the full in Sunday's thriller at Anfield, City looked content to settle for a dour, low-scoring win: the Liverpool match no doubt underlining that verve and elan may win you admirers, but not the title.
When, however, Fernandinho fired them into the lead after just one minute and 54 seconds it seemed that had banished the pain of Sunday, yet City never really built on that early platform.
It was a well-worked goal too, though it owed much to Cattermole's brain not having got into gear. The Sunderland midfielder was robbed by Alvaro Negredo who fed Aguero, and when the return pass came the Spanish striker stepped over the ball leaving Fernandinho free to plant his shot past Mannone at the near post.
The groans from the travelling Sunderland fans were almost audible, and their frustration grew as the visitors responded by forcing chance after chance only to see them go begging.
O'Shea was the leading culprit, putting two clear headers wide, while Borini dragged his shot wide of the far post when put through to face Hart one-on-one.
Fernandinho attempted to redress the balance for City but skied an equally-good opening after Mannone had only managed to parry Aguero's fierce strike.
Aleksandar Kolarov struck wide after a stirring run down the left as the first half ended with City looking to have fended off Sunderland's best thrust, and Gus Poyet wondering what might have been.
City's malaise continued in the second half as Sunderland's performance continued to impress.
Negredo and Aguero had half chances before Pellegrini sent on Stevan Jovetic in place of the Argentinian.
Jovetic looked impressive but could not add to City's single goal and instead it was Sunderland who made the breakthrough.
Poyet looked furious when Jack Colback failed to capitalise on a one-on-one chance by Hart, but that turned to delight when Emanuele Giaccherini burst down the felt and floated a beautiful cross for Wickham to thump home with glee.
Edin Dzeko held his head after missing the target, then came a dream moment for Sunderland fans as Giaccherini broke from his home half, delivered an excellent pass to Wickham who did not break stride as he buried his shot past Hart.
Humiliation was looming for City but in a frenetic finish Nasri forced an equaliser - the ball trickling agonisingly over the line after Mannone had got his fingers to it.
The Frenchman could have won it at the death too - but his shot went up in smoke and so too did City's title hopes.