But United will be wondering how they did not return to Bramall Lane with all three points.
They created a host of chances only to be denied by the Wolves' goalkeeper Wayne Hennessey. He pulled off a string of impressive saves but was also at fault for Beattie's goal when he spilled a Kyle Naughton cross.
Wolves struggled to live up to their normal high standards in front of their own fans as they failed to win at Molineux for only the third time in 13 home games this season.
Despite drawing first blood through Collins in the 19th minute, Wolves can count themselves lucky to have got to half-time on level terms as United were dominant in terms of chances created.
But for the heroics of Hennessey, United would have been well in control.
He denied Danny Webber, Beattie and Brian Howard twice before Wolves took the lead against the run of play through Collins.
United paid the penalty for giving the Scotsman space to rise and head home a corner from Michael Kightly.
But Wolves joy was short-lived as United were back on level terms just three minutes later.
Hennessey initially denied Beattie but when the ball was played back into the area by Naughton the Wales international keeper made a crucial error when he spilled the cross and Beattie pounced from close range.
United were unfortunate not to go on and take a lead into the interval as Nathan Dyer and Ugo Ehiogu were both frustrated by Hennessey.
Wolves' 29-goal strikeforce of Chris Iwelumo and Sylvan Ebanks-Blake found chances desperately hard to come by and their dismal day was summed up in the 48th minute when they both failed to score from inside the six-yard box - twice being denied by Ian Bennett.
United always looked the more likely side to score a decisive second goal only for Nick Montgomery to be frustrated by Hennessey and Beattie to then fire just wide eight minutes from time after outpacing Richard Stearman.