It was perhaps a fitting way for Ferguson to celebrate his milestone given the number of times his side have snatched victory in such a manner.
Mick McCarthy will not be the last manager to thrash about in frustration after United old-boy Sylvan Ebanks-Blake had looked to have snatched a deserved point for his team, cancelling out Park's opener in the first half.
However Park's run into the penalty area in the final seconds went unchallenged and he found the bottom corner of the net.
But it was not all good news for United, with the future of Owen Hargreaves again under scrutiny after the midfielder lasted just five minutes after starting for the first time since September 2008 before limping off with a hamstring injury.The subject of Hargreaves' fitness has been the subject of debate for a number of weeks now.
At one point his Colorado-based surgeon Dr Richard Steadman claimed he was ready to play, only for Ferguson to step in and explain the midfielder had suffered a setback in his recovery programme.
Only a week ago, Ferguson suggested he had no idea when Hargreaves would return, so the midfielder's presence in this afternoon's starting line-up was a big shock. His departure was probably less of a surprise.
After making a spirited start, the England star signalled to the bench he had a problem following an attempted cross from his right-wing station.
Hargreaves tried to continue but it was impossible and he made his way off, first to the touchline, then down the tunnel, a dejected figure, whose career is now thrown into fresh doubt, even though his latest setback is so obviously nothing to do with the dodgy knees that have kept him out for so long.
It is quite possible Hargreaves had gone before Fabio Capello, who had made the short trip south from Bolton, had even taken his seat. The introduction of Bebe was an obvious move given the options Ferguson had at his disposal.
Yet United's team sheet appeared woefully weak. Just 35 appearances, before today, for their front three, the vast majority of which had come as a substitute.
Wolves sensed their opponents were in trouble and once Richard Stearman had bravely blocked a Bebe shot, they pushed forward with intent.
Matt Jarvis was a particular threat and if Nemanja Vidic had diverted Nenad Milijas' 20-yard shot just inside, rather than outside, Edwin van der Sar's right-hand post, the stranded Dutchman could not have kept it out.
As it was, the game was still level when Darren Fletcher provided the pass of the first half, cutting in from the left before splitting the Wolves defence in two with a brilliant through ball that allowed Park to finish smartly.
After a disappointing start to the second period, Wolves finally gained their reward for all their industry when Ebanks-Blake was in the right place to intercept a Milijas shot, turn sharply round Vidic, then drive a fine shot through the legs of Van der Sar.
Under such circumstances, the introduction of Paul Scholes was an obvious move, so too that of Federico Macheda as Bebe joined that rare breed of substitutes who have been substituted themselves.
Yet the golden chance fell to a Wolves replacement as Steven Fletcher found himself with a clear sight of United's goal following an ill-advised attempted clearance by Vidic.
Instead of calmly finding the net, the Scotland international rushed his chance and scooped it over. Wolves thought they would at least be heading home with a point.
Then Park cut inside the area from the right wing two minutes into injury-time, and drove his shot past Hahnemann at the near post.