The three points will come as huge relief to Sir Alex Ferguson, who watched on from the stands as he completed his touchline ban.
He will have looked on for much of it in utter frustration as Sunderland came with damage limitation in mind after a week in which they lost manager Roy Keane.
They will feel aggrieved at failing to take a point that would have seen them climb out of the relegation zone.
But caretaker manager Ricky Sbragia will also be warmed by the spirit that was clearly missing against Bolton last week, which proved to be Keane's last game.
They were also indebted to Fulop, who came in for the injured Craig Gordon in one of four changes.
He was soon called into action as he denied Berbatov after a neat flick from Cristiano Ronaldo.
That was United of old - Phelan
Ronaldo had started off the game with the intention on marking a week in which he was named Ballon d'Or trophy with a star-studded performance, but ended it midway through the second half as he walked off injured.
A mazy run early on had earned United a free-kick on the edge of the box which he squared for Rooney to bring out another smart stop from Fulop.
Ronaldo almost stabbed in from close range after a corner was misjudged by everyone.
Rooney volleyed wide and some slack play from ex-United star Dwight Yorke let in Ji-Sung Park only for Fulop to come out swiftly to smother the danger.
Darren Fletcher twice threatened either side of half-time, but just failed to find the target with either effort.
Rooney again went close and Carrick had a low shot which Fulop got down to keep out.
Our gameplan nearly worked - Sbragia
Sunderland were close to a goal completely against the run of play when El Hadji Diouf escaped down the left and his centre almost deceived Edwin van der Sar, who made use of his legs to keep it out.
The United fans, who had seen their side put five past Blackburn in midweek, became increasingly agitated at the lack of goals but the chances continued to come.
Berbatov missed a glorious headed chance from a pinpoint Carrick cross and substitute Carlos Tevez dragged just wide after being set-up by Rooney.
Teemu Tainio threw his body in to block an Anderson effort as the game moved towards injury time.
But as Sunderland began to sniff a potential winner, United went forward and when Carrick's shot came back off the post, Vidic was in the right spot to send the home fans home happy.
Manchester United manager Sir Alex Ferguson:
"If we get within two or three points of the top two by the turn of the year, we will have a marvellous chance.
"It has not been easy for us but we have coped very well.
"Our form has been very good."
Sunderland caretaker manager Ricky Sbragia:
"We stuck in there, we were under severe pressure the whole game.
"Credit to the players, I thought we showed a good spirit, we worked ever so well and, on top of that, after Thursday's episode (Keane's resignation), the attitude was first class.
"A lot of the players came to the club because of Roy. We were disappointed. All the staff were disappointed and it came as a shock."
Man Utd: Van der Sar, Rafael Da Silva, Ferdinand, Vidic, Evra, Park (Tevez 57), Fletcher (Anderson 68), Carrick, Ronaldo (Giggs 68), Berbatov, Rooney.
Subs Not Used: Kuszczak, Neville, Nani, Evans.
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