However, United had to do it the hard way after going behind to a 27th minute goal from Kevin Davies.
But a superb strike from Louis Saha and a late winner from substitute Ruud van Nistelrooy made sure Sir Alex Ferguson's side snatched the points.
And victory means the title race is now well and truly open especially with the two sides due to meet at Stamford Bridge before the end of the season.
United were the better side, but they were shocked when Davies nutmegged Rio Ferdinand midway through the first half and the striker fired past Edwin Van der Sar.
But it took the visitors just six minutes to draw level when Frenchman Saha found the far corner with a wonderful shot with the outside of his boot.
And cue van Nistelrooy, dropped to the bench after his winner at West Ham in midweek, who was the visitors' hero.
The Dutchman found time and space after an excellent pass across the face of goal from Saha, and he was never going to miss from six yards out.
United could have won more convincingly, but for some excellent saves by Bolton keeper Jussi Jaaskelainen and some wayward finishing.
As early as the tenth minute United pressed and England international Wayne Rooney had the ball pinched off his toes by Jaaskelainen.
A minute later Cristiano Ronaldo crossed from the right but Rooney, unmarked on the spot, failed to control when he should have done better.
Ryan Giggs had a right-footed shot saved by Jaaskelainen and the keeper saved Rooney's rebound, before Ronaldo saw a shot deflected wide.
Bolton struck against the run of play before Saha levelled at the other end after an excellent throughball from Mikael Silvestre.
The restart saw both sides press for the lead and two minutes in Rooney fired wide from the edge of the box.
At the other end Jay-Jay Okocha saw a right-footed shot fly wide of the target and Abdo Faye was off target with a 30-yard drive.
In the 65th minute Okocha found space on the edge of the box, but Van der Sar palmed his shot away and then Rooney saw a right-foot shot easily saved by Jaaskelainen.
Gary Speed failed to hit the target with a left-foot drive and then fired wide at the far post just two minutes later as Bolton looked to cause a shock.
But van Nistelrooy's introduction, which nearly brought a penalty when he was fouled by Tal Ben-Haim, proved decisive.
The Dutchman caused all sorts of problems and, having nearly set up Ronaldo and Saha with chances, was in the six-yard box at the right time to fire home Saha's cross from the left.
Saha saw a shot charged down four minutes before time after a pass across the box from Ronaldo, before Okocha fired wide from distance a minute later.
In the third minute of stoppage time Rooney failed to hit the target, but by then the damage had been done and van Nistelrooy's late winner gave Ferguson plenty to smile about.