Fernandinho’s lightning-fast opener set the hosts off well but a Connor Wickham double threatened to deliver a hammer blow before the Frenchman grabbed a late leveller.
Fernandinho struck in the second minute, capitalising on a disastrous Lee Cattermole error, but the relegation-threatened visitors battled back superbly and deserved their second-half equaliser.
Connor Wickham got it, pouncing on the chance to volley home when Aleksandar Kolarov was out of position, and the striker then stole a second on the break in the 83rd minute, though Samir Nasri restored some pride with a goal at the death.
It came largely thanks to a mistake from Vito Mannone and the City midfielder would have wrapped up all three points but for a dreadful miss just moments later.
The result puts Gus Poyet’s side back to within six points of safety, with one game still in hand, but City’s title bid is left on the ropes, behind the Reds by the same margin even with one extra match to play.
City needed a response after their defeat on Merseyside and it came quickly, with two of Manuel Pellegrini’s five additions to the starting XI heavily involved in the build-up as the home side went ahead almost immediately.
Sergio Aguero slid the ball to Alvaro Negredo, whose dummy on the edge of the penalty area completely fooled defender Wes Brown – scorer of the own goal that led to his side’s 1-0 defeat against Everton on Saturday – and Fernandinho made no mistake in squeezing his strike between Mannone and the right-hand post.
Former Manchester United defender John O’Shea rose well to meet an Adam Johnson free kick from the right flank four minutes later but the Irishman wasted the opportunity by heading harmlessly wide of the target before nodding another effort narrowly over the crossbar.
City could have doubled their advantage when Fernandinho scooped a volley over the crossbar 11 minutes in but Sunderland were pressing well and might well have drawn level eight minutes later had Fabio Borini been less selfish and squared to a team-mate rather than go for goal himself from a narrow angle.
Despite the early breakthrough, City were struggling to impose themselves on their lowly opponents. Aguero was lucky to avoid serious injury following a dangerous tackle from Brown and the Argentine had calls for a penalty waved away before the break after going down under the challenge of O’Shea.
Substitute Stevan Jovetic tried to slot the ball beyond Mannone shortly after the hour mark but his effort was tame and comfortably collected by the Italian.
Joe Hart had to make himself big at the other end after 72 minutes when Jack Colback found himself through one-on-one but Wickham then turned the game on its head as he tapped home Giaccherini’s cross.
Wickham then fired an unstoppable effort into the bottom right-hand corner a few minutes later to deal City’s title hopes a second huge blow in the space of four days.
However, Nasri‘s late shot prompted the error from Mannone to earn City a point before the Frenchman blasted over the crossbar soon afterwards in a golden chance to take all the spoils.