Shorn of several key players through illness and fronted by a well-drilled Wolverhampton Wanderers side, the Reds negated a disjointed display to take the spoils through Ji-sung Park's injury-time winner.
The Korean, whose first-half opener had been cancelled out by ex-Red Sylvan Ebanks-Blake, slotted inside Marcus Hahnemann's near post in the third of four added minutes to send Old Trafford wild and extend United's winning run to six games.
That sequence included a similarly dramatic Carling Cup victory over Mick McCarthy's side, and the Midlanders can once again feel hard done-by after more than matching the Reds for long periods. Had substitute Steven Fletcher not blasted over from 10 yards late on, they might have been celebrating a famous victory.
Instead, United negated a display devoid of fluency to take the spoils when Park wound infield, shimmied and slipped a shot past Hahnemann. For long periods it seemed that the virus which had swept through Carrington would prove costly, while the mood inside Old Trafford was further dampened when surprise recall Owen Hargreaves was substituted with an early hamstring injury.
Michael Carrick and Dimitar Berbatov, almost certain starters, were claimed by the Carrington illness and joined a long list of absentees, while Paul Scholes was demoted to the bench - almost certainly because a booking would rule him out of the looming Manchester derby.