With seven matches to play, City, chasing their first title since 1968, moved on to 71 points, two behind United who could go five clear at the top if they beat lowly Blackburn Rovers at Ewood Park on Monday.
Arsenal's seven-match winning league run came to an end when they suffered a surprise 2-1 defeat at strugglers Queens Park Rangers, while Chelsea maintained their push for a top four spot with a 4-2 win at Aston Villa.
Wolverhampton Wanderers are beginning to look doomed following their seventh successive home league loss as they went down 3-2 against Bolton Wanderers.
That result left Wolves on 22 points, six adrift of Blackburn, QPR and Wigan Athletic, who continued their revival with a 2-0 win over Stoke City.
Manchester City manager Roberto Mancini told Sky Sports: "It was a crazy game" and said he had no real explanation why his team's form had dipped after they led the table for almost five months until their defeat at Swansea City three weeks ago.
"We didn't play a good game today. They had a lot of chances, we made some mistakes and that's it - we can do nothing at the moment."
Asked what was going wrong, he replied: "I don't know - we have been really unlucky. We lost two or three important players and we didn't play well, but at least at the end we scored twice and got a point."
Although Sunderland did not win, they ended City's perfect home record following 15 straight league wins this season, after taking the lead through Sebastian Larsson after 31 minutes with a shot from the edge of the box.
City replied with a Mario Balotelli penalty after 43 minutes following a foul on Edin Dzeko but a Nicklas Bendtner header put Sunderland 2-1 ahead before halftime and Larsson made it 3-1 10 minutes into the second period.
Sunderland still led with five minutes to play before Balotelli pulled one back and Aleksandar Kolarov, who had an angry exchange with Balotelli over a free-kick earlier in the second half, scored to save a point a minute later.
Lowly QPR, battling against an immediate return to the Championship, were too good for Arsenal at Loftus Road, going ahead through Adel Taarabt's first Premier League goal with a drilled shot after 22 minutes.
In-form Theo Walcott equalised for the visitors in the 37th but Arsenal, who have been in superb form in recent weeks, lost their way in the second half.
Samba Diakite scored QPR's winner with a first time shot - his first goal for the club -- leaving Arsenal third in the table on 58 points, three ahead of Tottenham Hotspur.
Spurs can move level on points with their arch-rivals if they beat Swansea City at White Hart Lane on Sunday.
"We had an apparent superiority but it was only apparent because I felt we lacked a lot today," said Arsenal manager Arsene Wenger.
"We made mistakes and our performance was not good enough. We lacked the extra gear, and when you lack that you don't win games."
QPR boss Mark Hughes told Sky Sports: "I'm very proud of the players who have beaten a very accomplished Arsenal side who in recent weeks have been the in-form team in the Premier League.
"We showed a lot of discipline and resilience to see the game out. We had a fantastic night here recently when we beat Liverpool but today was even better."
Chelsea won on an emotional day at Villa Park, after allowing Aston Villa back into the game in the closing stages before taking all three points with two late goals.
Villa captain Stiliyan Petrov, who has been diagnosed with acute leukaemia, watched the game with his family from the directors box and was given a minute's applause by fans in the 19th minute - which matches his shirt number.
Petrov, who begins treatment for his illness on Monday, looked on as Chelsea went 2-0 ahead through Daniel Sturridge and Branislav Ivanovic, then recovered from a Villa fightback to win 4-2 which took them within two points of Spurs.
Villa, fielding a young, inexperienced team, equalised with goals from James Collins and Eric Lichaj but Chelsea pushed on to take all three points with a second for Ivanovic and one from Fernando Torres, who got his first league goal since Sept. 24.
Villa manager Alex McLeish, whose side are only five points above the relegation zone, told Sky Sports he was not surprised by the show of emotion for his 32-year-old skipper Petrov.
"It's a measure of how popular the guy is," he said, "Not only at this club but at his former club Celtic, while the Bulgarian nation will be rooting for him.
"He is a determined guy and he says he will fight it and beat it. It was a good moment when he came in the dressing room."
