Manchester United's shock 3-2 defeat by bottom team Blackburn on Saturday handed City the chance to pull clear at the top but the cross-town rivals remain locked together on points at the halfway stage of the season after Ji Dong-Won's dramatic winner at the Stadium of Light.
Four seconds of the three minutes of stoppage time were remaining when the South Korea striker tapped into an empty net after rounding City goalkeeper Joe Hart.
The impact of City's defeat will also be felt in London, with third-place Tottenham six points behind with a game in hand despite its 1-1 draw at Swansea on Saturday.
Arsenal is three points further back in fourth while even Chelsea, which was upset 3-1 at home to Aston Villa on Saturday, and Liverpool might still feel in contention 11 points off the lead.
In Sunday's other game, Everton climbed into the top half of the table by beating West Bromwich Albion 1-0 thanks to substitute Victor Anichebe's 87th-minute winner.
Ji's goal, which came with a suspicion of offside, came even later to continue City's recent wobbles in the league.
After looking irrepressible early in the season in its hunt for a first title since 1968, Roberto Mancini's side has won only two of its last five matches.
Even the goals, which flowed in record style for the first four months of the campaign, have dried up, with the Sunderland defeat coming hot on the heels of a 0-0 draw at West Brom on Monday.
"We deserved to win this game," Mancini said. "It's incredible ... I don't know how many chances we had."
Micah Richards missed the best of them, the substitute defender heading downwards and onto the bar with the goal at his mercy in the 88th minute. Earlier, Edin Dzeko had wasted a number of chances in both halves, crashing a shot against the bar with one in the 34th minute.
"We knew we were going to have withstand ferocious pressure from Manchester City. We did it and we did it remarkably well," said Sunderland manager Martin O'Neill, whose team climbed three places to 13th.
The O'Neill effect has lifted the gloom at Sunderland, with the team winning three of its five matches since the Northern Irishman replaced Steve Bruce as manager at the start of December.
"We've got the belief going into games that we're going to win now," Sunderland captain Lee Cattermole said.
City will look to bounce back when it hosts Liverpool on Tuesday, when Mancini will no doubt recall Sergio Aguero and David Silva to the starting lineup after the attacking pair were used as second-half substitutes against Sunderland.
City also play Tottenham in the league this month and has a mouthwatering FA Cup third-round match at home to United to come on Sunday.
Anichebe came off the bench to grab his first goal since March 2010, pouncing on a poor defensive header by West Brom midfielder Paul Scharner to score from close range.
It was the Nigeria striker's first appearance since injuring himself on international duty at the start of September.
"He's not even had a reserve game," Everton manager David Moyes said. "He's a big-time player because of what he can do and what he brings to us."
The win lifted Everton three places to ninth, extending the team's unbeaten streak to four matches.
West Brom remains the league's lowest scorers at home with just seven goals in 10 matches at the Hawthorns.