United burst out of the blocks to score after just 37 seconds when Javier Hernandez swept in a delightful Park Ji-sung pass and the hosts doubled their lead after 23 minutes when captain Nemanja Vidic headed in a perfect cross from Ryan Giggs.
A Frank Lampard tap-in after 69 minutes gave Chelsea hope but United deservedly held on and need just one point from their final two games against struggling Blackburn Rovers and Blackpool to secure the title.
A packed Old Trafford crowd rose to their feet before the final whistle to celebrate and United manager Sir Alex Ferguson bowed to them as they chanted "Glory, glory, Man United" after one of their team's most dazzling performances of the season.
"It's a massive step forward for us. Mathematically we have not won the title but we are nearly there," Giggs told Sky Sports.
"We know we are capable of playing good football and we knew we had to keep attacking as one goal is not enough against a team like Chelsea. It was a great start and it would have been easy for us to take our foot off the pedal but we didn't."
United, unbeaten at home since April 2010 when Chelsea won 2-1 on the way to winning the title by a single point, were determined not to let the London side undo them for a second successive year.
Having rested most of his first-choice players in Wednesday's easy Champions League semi-final second-leg win over Schalke 04, Ferguson fielded fresh legs who were so fired up they literally could not wait to score.
With the first move of the game, Giggs put Park through and the South Korean sent an exquisite pass that goal poacher-in-chief Hernandez slotted past Petr Cech to set the tone of the game.
HUGE MOUNTAIN
Park's energy was behind several more United bursts forward as the hosts turned in a sizzling all-round performance that will have impressed Champions League final opponents Barcelona before the May 28 showdown at Wembley.
Wayne Rooney unleashed a couple of long-range efforts that Cech was forced to save in an unrelenting United opening period of pressure before Park's scorching shot was parried behind for the corner that led to the second goal.
Giggs sent the corner short and quickly received it back to lift in a cross for Vidic to head home and give Chelsea a huge mountain to climb.
The London side, having climbed several big peaks to get back into the title race after a mid-season slump that put them 15 points behind the leaders, tried to fight back with chances for Salomon Kalou and Didier Drogba.
Lampard's scrappy goal mirrored much of Chelsea's play, as he stuck a foot out to push in a Branislav Ivanovic flick .
The champions simply could not match the pace of winger Antonio Valencia, who regularly outwitted Chelsea left-back Ashley Cole, or the fluid combinations between Park, Rooney and Hernandez.
Chelsea were lucky to avoid conceding a penalty when Lampard handled in the area and they could not raise their game enough as Ferguson edged closer to a 12th Premier League title.
Afte
