Substitute Louis Saha scored the winner as Manchester United edged out Roy Keane's Sunderland side.
Saha got the winner at Old Trafford
Saha headed in at the near post from Nani's corner with 18 minutes to go after former United favourite Keane's side had frustrated the champions.
Black Cats keeper Craig Gordon had earlier brilliantly denied Saha while Nemanja Vidic volleyed over.
Sunderland rarely looked like getting on the scoresheet and Owen Hargreaves was close to adding a second.
United were still some way from their fluent best and Keane, who was given a rapturous reception from the home fans on his first appearance at Old Trafford as a manager, will be disappointed with the way the game was decided.
It was a poor goal to concede, with Saha allowed a free header and Gordon blotting his otherwise impressive copybook by coming for the cross and getting nothing but fresh air.
Until then Sunderland had limited the home side to only a handful of attempts in goal, with their 4-5-1 formation proving a tough barrier to break down.
When United did manage to find the target, Gordon proved a safe pair hands to hold efforts from Anderson and Chris Eagles.
United's best chance of the opening half came right at the end when a well-worked free-kick from Nani provided Paul Scholes with a shooting chance 25 yards out, but his strike deflected off Danny Collins and flashed just wide.
Anderson's uninspiring debut came to an end at half-time, as he made way for Saha - and the Frenchman's introduction immediately livened up United's attack.
He found a hole in the Sunderland defence before lashing a shot that was headed for the bottom corner, but Gordon was more than equal in pulling off a stunning one-handed save.
Sunderland's Ross Wallace gets close to debutant Anderson
From the corner Vidic arrived late to volley over unconventionally.
A Hargreaves long-range shot troubled Gordon before he gathered at the second attempt, taking a smack in the face from Scholes in the process.
Then came Saha's goal and despite Sunderland enjoying plenty of possession in the final quarter of an hour they rarely looked like summoning an equaliser.
It was Keane's name that the fans were chanting as he and United boss Sir Alex Ferguson walked off the pitch together after the full-time whistle.
But it was the master who got the better of his young apprentice this time.
Manchester United manager Sir Alex Ferguson:
"The first half our passing was far too slow and we were not making many chances.
"Louis Saha gave the players a target. He's very much needed, with his speed and his strength we've missed him so we're delighted to have him back.
"I thought we deserved to win the game but it was a long day."
Sunderland manager Roy Keane:
"When you lose to a set-piece it's very frustrating. One lapse and you can lose the game.
"I'm delighted with the overall performance. It would have been nice to test their goalkeeper a bit more but overall I'm delighted with the players' efforts.
"The United fans were fantastic - and the Sunderland fans were too - but we're still leaving with no points."
Man Utd: Van der Sar, Brown, Ferdinand, Vidic, Evra, Eagles (Fletcher 66), Hargreaves, Scholes, Nani (O'Shea 84), Anderson (Saha 46), Tevez.
Subs Not Used: Kuszczak, Carrick.
Goals: Saha 72.
Sunderland: Gordon, Nosworthy, McShane, Higginbotham, Collins, Leadbitter, Yorke, Etuhu (Miller 82), Wallace (Stokes 82), Chopra, Jones (Murphy 69).
Subs Not Used: Ward, Kay.
Booked: Leadbitter, Chopra.
Ref: Martin Atkinson (W Yorkshire).