Beaten 3-2 at Liverpool on Sunday, City were bidding to close to within four points of Brendan Rodgers’s side in the first of their two games in hand.
Fernandinho’s 2nd-minute goal at the Etihad Stadium put City on track.
But after Connor Wickham scored twice in the last 17 minutes, the hosts needed a fortuitous 88th-minute equaliser from Samir Nasri just to rescue a point.
The result left City six points below Liverpool in third place and although Manuel Pellegrini’s side still have a game in hand, the title is inching ever closer to Anfield.
“It is not enough, because we have Liverpool and Chelsea on top of the table and we needed to add three points,” said City coach Pellegrini.
“We will see in the future what will happen, but our chances are less.
“When it no longer depends on what you can do it is very frustrating, but we must finish the season the way we have done practically the whole season.”
City were without injured midfielders Yaya Toure and David Silva, but top scorer Sergio Aguero returned to their starting line-up alongside Alvaro Negredo as Pellegrini made five changes to the team that lost at Liverpool.
The hosts made an ideal start, with Negredo winning the ball back and finding Aguero, whose pass enabled Fernandinho to open the scoring from eight yards.
Fernandinho should have made it 2-0 when he blazed over from a Pablo Zabaleta knock-down after Vito Mannone had saved from Aguero, but Sunderland then created several chances to equalise.
John O’Shea twice headed off-target from set-pieces, while Fabio Borini and Adam Johnson each fired efforts narrowly wide before half-time.
A deflected Aguero effort that Mannone saved comfortably was the best that City could muster in the early stages of the second period and in the 73rd minute they were punished.
– Wickham at the double –
Emanuele Giaccherini sent a cross into the City box from the left and Wickham steered a volley past Joe Hart to register his first league goal since 2011.
Ten minutes later Wickham struck again, beating Hart at his near post after a Sunderland counter-attack and leaving Gus Poyet’s men on the verge of avenging their loss to City in the League Cup final.
It was not to be, as Nasri’s long-ranger somehow squirmed past Mannone and over the line, but the Frenchman’s failure to convert a gilt-edged opportunity moments later meant that it was still a costly night for City.
“We conceded a goal after two minutes at Manchester City and every single person in the world expected us to lose from there,” said Sunderland manager Poyet.
“But we passed the ball and created chances. We kept believing.”
While Liverpool’s fans exulted in City’s misfortune, it was a different story in the other half of the city, as Everton fell to a 3-2 loss at home to Crystal Palace that prevented them from reclaiming fourth place from Arsenal.
Victory would have sent Roberto Martinez’s side back into the Champions League places, but they fell behind in the 23rd minute when Marouane Chamakh teed up Jason Puncheon to score.
Second-half goals from Scott Dann and Cameron Jerome completed victory for Tony Pulis’s side, with substitute Steven Naismith and Kevin Mirallas replying in vain for the hosts.
“It’s a real disappointment, a result which is hurtful,” said Martinez, whose side had won their seven previous games.
“We will try and get as many points as we can. It doesn’t change anything. We have had a magnificent season and we have incredible potential in this squad.”
Defeat left Everton in fifth place, one point below Arsenal, ahead of their home game with Manchester United on Saturday, while Palace have now reached the 40-point mark usually synonymous with survival.
“I think we are safe,” said Pulis, who succeeded Ian Holloway as Palace manager in November.
“My first game, when we went to Hull, we had four points, so to get to 40 points is a fantastic achievement for this group of players.”