Former United defender Wes Brown, on his first return to Old Trafford since leaving in the summer, put the ball into his own net just before halftime and the three points lifted United back into second place in the Premier League.
The game was never a classic but United did enough to win on the day that chief executive David Gill announced the north stand at Old Trafford had been renamed the "Sir Alex Ferguson Stand" and that a statue of the 69-year-old Scot was being commissioned to mark his achievements for the club since he took over on November 6 1986.
Ferguson has brought 37 trophies to Old Trafford and, although they are not leading the title race now, they are in contention for a 13th championship since 1993, after moving to within two points of leaders Manchester City who were playing at Queens Park Rangers in the late kick-off.
"I thought we were anxious but in the second half we improved, although the last 15 minutes was torture," Ferguson told Sky Sports.
"I don't know whether it was down to the way Sunderland played, or the occasion; these emotional occasions, which it was for me today, sometimes get through to them."
Manchester City - who beat Queens Park Rangers 3-2 at Loftus Road in an entertaining late game - lead the table with 31 points from 11 matches, followed by United on 26 from 11, Newcastle on 25 from 11 and Chelsea, who won 1-0 at Blackburn Rovers with a Frank Lampard header, fourth on 22.
City came from a goal down as they faced their strongest domestic test of the season in West London. Jay Bothroyd put the hosts ahead with a header from Joey Barton's free-kick, and the Hoops would have doubled their lead but for fine goalkeeping by Joe Hart - and the woodwork.
But Heidar Helguson levelled for QPR when he inadvertently knocked Bothroyd's header over the line, the officials correctly waving away City's appeals for offside with replays showing Stefan Savic played the Icelandic level.
City would not be denied though, with Yaya Toure heading home Alexandr Kolarov's cross to seal the win for the leaders, who are unbeaten in the league this season.
United slipped down to third for a few hours after Newcastle United stretched their unbeaten league run from the start of the season to 11 matches with a 2-1 home win over Everton in a lunchtime kick-off.
"We lost two key players but the guys who came on did very well and it shows the strength in depth. We showed another side today - we defended absolutely brilliantly, that was one of our best defensive displays of the season."
Arsenal continued their revival by beating West Bromwich Albion 3-0 for their fifth straight league win at the Emirates with Robin van Persie among the scorers, taking his tally to eight goals in his last four league games and 29 in his last 28.
Aston Villa beat Norwich City 3-2 in a superb match at Villa Park with Darren Bent scoring twice and Gabriel Agbonlahor once to underline their claims for inclusion in the England squad being announced by Fabio Capello on Sunday for international friendlies against world champions Spain and Sweden this month.
Liverpool had a late Dirk Kuyt goal disallowed for offside and were held to a 0-0 draw by Swansea City at Anfield, a huge improvement on Swansea's last visit to Anfield for an FA Cup tie in 1990 when they lost 8-0.