Trailing to Bruno N'Gotty's 61st minute goal and rescued from going further behind by a series of saves by Fabien Barthez, United looked jaded and certainly second best to a Wanderers side fighting to get away from the relegation zone.
Unfortunately after looking solid at the back with new French loan signing Florent Laville shoring up the back four they were caught out in the last minute when David Beckham's cross was swept in by Solskjaer at the near post.
In the ninth minute Wanderers had what looked to be a worthwhile penalty claim turned down as Ivan Campo appeared to be pulled back as he moved onto Simon Charlton's ball into the area.
Barthez was then happy to get a fingertip to a Youri Djorkaeff free kick that looked destined to be heading to the far top corner.
United were also helped by some poor finishing from Bernard Mendy, Ricardo Gardner and Campo, although Barthez had to deny Okocha three minutes before the break.
The visitors the n had their best chances of the half with Brown heading over and Jussi Jaaskelainen having to react quickly to keep out a Florent Laville back pass.
Wanderers would have had the lead eight minutes after the break but for Barthez who somehow kept out a close range header from Henrik Pedersen after Campo's flick on.
Wanderers’ efforts deserved a goal and they were finally rewarded on the hour when N'Gotty bundled in Djorkaeff's free kick from close range.
Nevertheless inside three minutes United should have been level but Jaaskelainen pulled off a good save from Keane to preserve his side's lead.
The strain of the Champions League, FA Cup ties and the Premiership appeared to be telling on United who brought on Butt for Veron eight minutes from time.
In the end a mistake by Okocha when he gave the ball away to Beckham settled the issue, the England captain's cross being swept in by Solskjaer a minute from time.