The South Korean's brave diving header on the hour earned United a priceless victory at Old Trafford and also inflicted a 10th league defeat of a disappointing season on the visitors.
United, who had been beaten by the Merseysiders in their last three outings, finally put an end to that dismal run.
In the way Liverpool had done in the corresponding fixture last season, United had to come from behind after Fernando Torres put the visitors ahead in the fifth minute with his 18th goal of the season.
Steven Gerrard pounced and a loose ball in the centre circle to feed Dirk Kuyt on the right.
Kuyt took the ball out to the byline before producing the perfect cross for Torres to head home from eight yards when he ghosted in between Rio Ferdinand and Gary Neville.
But United hit back with an equaliser seven minutes later.
As Antonio Valencia cut in from the right, he was tugged back by Javier Mascherano.
Although the foul began outside the penalty area, the Argentinian continued to hold on to Valencia's arm as he moved into the box and then went down.
Referee Howard Webb pointed to the penalty spot and up stepped Wayne Rooney.
The England star's right-footed spot kick to Pepe Reina's left was brilliantly parried by the Liverpool goalkeeper but the rebound fell perfectly for Rooney, who tucked it home from six yards for his 33rd goal of the campaign.
In a game of few chances, the crucial moment came on the hour.
Rooney found Darren Fletcher on the right and his cross into the centre saw Park glide in between Daniel Agger and Glen Johnson to score with a superb diving header.
Park could have scored before his goal with one of two headers - the first coming midway through the first half which was a free one from Valencia's pinpoint cross from the right byline.
Liverpool created little to trouble Edwin van der Sar, although Torres' mis-kick from ten yards in the dying seconds sat up nicely for substitute Yossi Benayoun but the Israeli's weak header from six yards fell tamely into the keeper's arms.