The win stretched Wolves' unbeaten run to 18 games - the longest in the Championship this season.
In a game where only pride was at stake for both sides, defending left a lot to be desired and that contributed to flurry of goals.
Wolves broke the deadlock through central defender Joleon Lescott only for midfielder Alan Quinn to draw United level.
Teenage forward Leon Clarke fired Wolves back in front before a strike from Scottish international striker Andy Gray once again secured United a foothold in the game.
But there was no way back for Neil Warnock's United side after half-time as substitute Cooper and Kenny Miller, with his 20th goal of the season, struck in the opening 15 minutes of the second period.
Lescott sparked a frantic spell of four goals in the space of just 26 minutes when he broke the deadlock in the 11th minute.
He profited after a fierce drive from Ki-Hyeon Seol was palmed out by goalkeeper Paddy Kenny. The loose ball fell invitingly to Lescott who drove home his first Molineux goal of the campaign and his fourth of the season.
However, Wolves' joy was to prove to be short-lived as United dragged themselves level just two minutes later when Quinn beat goalkeeper Michael Oakes from fully 20 yards after being picked out by a pass from Phil Jagielka.
When Jagielka then hit the post in the 21st minute, United looked set to take charge of affairs. But it was Wolves who struck next when Clarke exchanged passes with Miller and beat Kenny with an angled shot for his third goal in four games and his eighth of the season.
Kenny then denied Clarke a second goal before United hauled themselves level again. This time it was a classy piece of finishing by Gray who was picked out by a Danny Webber pass and coolly beat Oakes with a low drive to take his tally for the campaign to 18.
Wolves boss Glenn Hoddle reshuffled his side at half-time by taking off Seyi Olofinjana and Rob Edwards and replacing them with Cooper and Mikkel Bischoff.
The move took just five minutes to pay dividends with Cooper firing Wolves back in front after the hard-working Miller turned provider again.
He held off a challenge from Leigh Bromby and curled a pass into the path of the onrushing Cooper who saw his shot take a slight deflection of Michael Tonge before flying past Kenny for his first goal since the clash with Millwall on December 7.
Miller was then rewarded for all his hard work on the hour when Rohan Ricketts and Clarke combined to set up the Scottish international to side-foot home from eight yards.