United moved to 69 points from 31 games, displacing overnight leaders Arsenal who slipped back to second with 67 points. Chelsea, third on 64 points, will go above Arsenal if they win at Blackburn Rovers in a later kickoff.
Liverpool struck first in glorious spring sunshine at Old Trafford when an unmarked Fernando Torres headed in Dirk Kuyt's cross after only five minutes but their lead was short-lived.
United drew level seven minutes later after Javier Mascherano conceded a penalty for a foul on Antonio Valencia and, although Rooney's spot-kick was saved by Pepe Reina, he pounced on the rebound to score his 33rd goal this season.
Park scored what proved to be the winner when he converted Darren Fletcher's cross from the right with a brave diving header after 60 minutes.
Fulham host Manchester City in the afternoon's other match.