Scholes finally broke the resistance of a dogged Wolves side in the 72nd minute.
United made hard work of what was only the third win in their last seven away games as relegation-threatened Wolves more than held before Scholes struck.
In fact, Wolves will be wondering what might have been as Stephen Ward wasted a golden chance to give them a 35th minute lead after an impressive first-half display from Mick McCarthy's side.
Ultimately, their lack of a cutting edge was again their downfall as they failed to score for the 13th time in 28 league games this season.
Their problems in attack were summed up in added time when substitute Sam Vokes somehow failed to hit the target from six yards with only Edwin van der Sar to beat.
With United missing the injured Wayne Rooney and Michael Owen, Wolves looked set to hold out for what would have been a priceless point before Scholes struck.
But they were undone when they failed to deal with a cross from Nani and Scholes side-stepped a couple of challenges before beating Marcus Hahnemann from close range.
McCarthy's side were far from overawed by their illustrious opponents and made their intentions clear after five minutes when Kevin Doyle fired wide.
That did spark a spell of United pressure with Darron Gibson proving to be their dangerman.
He was inches wide in the 14th minute when he latched on to a Nani free-kick that had been deflected into his path by Dimitar Berbatov.
Former Wolves' loanee Gibson was then denied by Hahnemann before the Irishman shot wide when well placed.
But Wolves more than carried a threat of their own and Kevin Doyle was denied by van der Sar after a neat move involving Matt Jarvis and former United player Dave Jones.
Jarvis then teed up boyhood United fan Ward for the chance of the half in the 35th minute with a pinpoint left-wing cross.
Ward had ghosted forward from left-back to find himself on the edge of the six-yard box only to place his header straight into the hands of van der Sar.
It was a costly miss by Ward as United stepped up their game in the second half and it did seem only a matter of time before they broke the deadlock.
Patrice Evra should have put United in control when he just failed to turn home Gibson's pass from six yards.
Fortunately for United, Scholes proved to be more clinical as he put United firmly on course to retain their Premier League title and leave Wolves only out of the drop zone on goal difference.