With Chelsea having moved four points clear at the top of the table following a 2-0 victory at Liverpool earlier in the day, Sir Alex Ferguson's side needed to win on Wearside to keep the title race alive heading into the final weekend of the season.
But while the Red Devils were far from at their best despite the return to the starting line-up of Wayne Rooney, they picked up the required three points to maintain their pursuit of a fourth successive league title heading into next weekend's final game of the season at home to Stoke City.
United were rarely threatened at the back but were indebted to Nani after his 28th minute incisive finish proved decisive.
Rooney tested home goalkeeper Craig Gordon inside five minutes while Ryan Giggs' follow-up was blocked by Phil Bardsley.
Giggs rattled the corner of post and crossbar soon after as the visitors pressed for an early advantage, but Steed Malbranque sent out a warning with a rising shot which Edwin van der Sar in the United goal did well to tip over.
The warning appeared to be heeded when United surged ahead midway through the period.
Giggs, Rooney Dimitar Berbatov and Darren Fletcher were all involved in the move, which ended with the Portuguese winger curling a low, right-foot drive into the far corner of the net with the outside of his boot.
Nani was thwarted by Gordon in the early stages of the second half after being set-up by Fletcher.
Berbatov was next to waste a golden chance when he snatched at a volley before seeing a header hit the woodwork after deflecting off United old-boy Kieran Richardson
Michael Turner cleared an effort from substitute Michael Carrick off the line before the Red Devils - helped by fit-again England captain Rio Ferdinand coming off the bench - held firm in the face of some late home pressure.
United must now hope that Chelsea slip up at home to Wigan Athletic next Sunday and they can overcome Stoke City if the Premier League trophy is to remain at Old Trafford for another season.