The workaholic South Korea midfielder, whose first-half effort had been cancelled out by Wolves substitute Sylvan Ebanks-Blake, drifted in from the right in the 93rd minute and planted a shot past helpless keeper Marcus Hahnemann.
It raised the roof at Old Trafford and spared United a sixth draw as they try and stay on the tail of leaders Chelsea whose lead in the title race has now been cut to two points.
United's last-gasp victory was soured, however, by the sight of former England midfielder Owen Hargreaves limping off five minutes into his first start for more than two years.
Asamoah Gyan's double gave Sunderland a 2-0 home win over Stoke City while Fulham equalised late in a 1-1 draw with visiting Aston Villa. Blackburn Rovers beat Wigan Athletic 2-1.
Manchester United welcomed back Hargreaves after the Canadian-born player's battle with chronic tendinitis in both knees but his appearance was short-lived as he hobbled off with a hamstring strain after a run down the right flank.
With Michael Carrick and Dimitar Berbatov having fallen victim to an illness that swept United's training ground this week, Nani injured and Wayne Rooney heading for the United States to continue his rehabilitation from injury, the hosts were toothless in attack and indebted to the lively Park.
"Right on halftime and right on the final whistle are amazing times to score," said United manager Alex Ferguson, whose team's trademark over the years has been late goals.
"But Ji's in great form actually, he's been one of our best players in recent weeks," he told MUTV.
