Van Nistelrooy, starting from the bench again despite netting the winner against West Ham in midweek, converted Louis Saha's cross on 79 minutes to seal a 2-1 win at the Reebok Stadium and breathe new life into the title race.
Saha had cancelled out Kevin Davies's opener for Bolton.
"It's our best result of the season, maybe," United manager Alex Ferguson told Sky Sports after his side inflicted a first home defeat on Bolton in 22 games in all competitions.
"It was (a performance) of determination and grit because the pitch was not very good ... we kept on plugging away until we got the winner."
Chelsea were frustrated by relegation-threatened Birmingham City, the Londoners held at St Andrews in a lunchtime kickoff.
With six games to play, Chelsea have 79 points from 32 games with United on 72. Third-placed Liverpool (64) play at West Bromwich Albion in a late kickoff (1615).
Thierry Henry scored twice in Arsenal's 5-0 demolition of Aston Villa, who are being dragged into the relegation dogfight, while Tottenham Hotspur had defender Michael Dawson sent off in a 3-1 defeat at Newcastle United.
Spurs remain in the fourth Champions League place on 55 points and bitter rivals Arsenal moved into fifth, two behind after running Villa ragged at Highbury.
At the bottom, Portsmouth's third successive win, 3-1 over Fulham at Craven Cottage, gave the south coast side hope of escaping the drop. Bottom side Sunderland drew 2-2 at Everton and will be relegated if West Brom defeat Liverpool.
Van Nistelrooy has endured a frustrating few weeks at Old Trafford, Ferguson preferring Frenchman Saha to play alongside Wayne Rooney.
The Dutchman was again left out of the starting side but gave Ferguson food for thought with a typically clinical finish, his 150th goal for the club.
"We know when he comes on he's going to do it because he's the best finisher in the game," said Ferguson. Van Nistelrooy and Henry lead the league goalscorers' list with 21 each.
UNCONVINCING DISPLAY
Chelsea manager Jose Mourinho was unhappy with another unconvincing display away from home and his side have won just one from their last five on their travels.
"I am concerned, I want to win every game, I'm not happy with the performance and result," he told Sky Sports.
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Birmingham, third from bottom and reeling from shipping 10 goals in their last two games in league and Cup, defended competently and produced the game's best moment when Olivier Tebily forced Petr Cech into a fingertip save from long range.
Chelsea almost stole the points at the death but Argentine Hernan Crespo wasted two good chances while defender Ricardo Carvalho headed over.
The leaders also had two goals ruled out, Mourinho lamenting the decision to nullify Asier Del Horno's 50th minute header after Carvalho, in an offside position, was deemed to be active.
"We scored a goal ... it was not offside. It was a clear goal according to the rules. I don't want to say more about it because every single word I say in this country the next day is a nightmare."
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