With United not in action until Monday, City knew that it could have drawn level on points with the defending champions with a Premier League-record 21st straight home win.
Instead, City needed two goals in the last six minutes to salvage a draw.
Sebastian Larsson scored either side of a goal from Nicklas Bendtner to give Sunderland a 3-1 lead before Mario Balotelli hit his second goal of the game for City and Aleksandar Kolarov equalized in the 86th minute.
Third-place Arsenal lost 2-1 at Queens Park Rangers and Chelsea scored twice in the last six minutes to win 4-2 at Aston Villa. Fernando Torres scored his first Premier League goal in six months as Chelsea kept up its challenge for a top-four finish.
City's second straight draw means United could go five points clear with seven games remaining if it beats Blackburn on Monday. City rallied for last weekend's 1-1 draw at Stoke and needed an even bigger comeback against Sunderland, which beat City 1-0 in January.
Larsson scored with a low shot into the corner from the edge of the area in the 31st and, although Balotelli leveled with a contentious penalty awarded for Craig Gardner's challenge on Edin Dzeko, City trailed at halftime for the first time this season after Bendtner headed in Stephane Sessegnon's cross.
Larsson made it 3-1 with a far-post finish from Bendtner's cross and City's frustrations showed as Balotelli and substitute Carlos Tevez apparently argued over who would take a free kick. Kolarov eventually took it.
But Balotelli reduced the deficit with a long-range shot and Kolarov smashed in an equalizer from substitute David Pizarro's set up.
City has 71 points to United's 73. Arsenal has 58 after former Tottenham midfielder Adel Taarabt, with his first Premier League goal, and Samba Diakite scored for QPR. Theo Walcott got Arsenal's reply.
With captain Stiliyan Petrov watching from the stands following his diagnosis with leukemia, Villa fought back from 2-0 down to 2-2 before Branislav Ivanovic and Torres clinched a win that moved Chelsea two points behind fourth-place Tottenham.
Daniel Sturridge and Ivanovic put Chelsea ahead before James Collins and Eric Lichaj brought Villa level.
Petrov was visibly emotional as he waved from the stands to the fans giving him a standing ovation.
It was Chelsea's sixth win in eight games under interim coach Roberto Di Matteo, although Spurs can restore its lead over its London rival to five points if it beats Swansea on Sunday.
Everton is seventh after a 2-0 win over West Bromwich Albion and Clint Dempsey scored his 13th Premier League goal of the season to help Fulham beat Norwich 2-1.
Also, Wigan boosted its chances of avoiding relegation with a 2-0 win over Stoke, and last-place Wolverhampton Wanderers looks sure to be demoted after a 3-2 home defeat against Bolton.