In reality, a poor end-of-term match played at a low intensity only came to life in the final five minutes, when Chelsea's Juan Mata gave his side three vital points with his 19th goal of the season.
United's Rafael da Silva then saw a straight red card for tangling with David Luiz, the Brazilian becoming the first United player to be dismissed in a league game this season, with the consequence the resulting suspension means he will miss the opening game of next term.
Sir Alex Ferguson, the United manager, said: "He [Rafael] retaliates, but he [David Luiz] quite clearly elbows him twice then rolls about like a diving swan.
"Chelsea deserved to win, we can't complain, but we expected a better performance. After the goal, we had no time to get back in it."
After Ferguson's side confirmed their 20th league title two weeks ago, it was inevitable that their intensity would drop for their final four games. Despite several players being given a rare chance to impress, United were poor, but if their lethargy was understandable, Chelsea's was not.
Rafa Benitez's side still have much to play for. A top-four finish was not assured and they have a Europa League final against Benfica in Amsterdam on May 15 to look forward to, where they could become the first English team to win all three major European competitions.
The injured Eden Hazard aside, Chelsea were at full strength as they pushed to regain third position from Arsenal and move three points clear of fifth-placed Tottenham Hotspur, who they play on Wednesday.
United made several changes: David de Gea, Rio Ferdinand and Wayne Rooney all began the game on the bench, with Anders Lindegaard, Anderson and Tom Cleverley starting, the latter for the first time in the league since February 10th.
Both teams had limited goal efforts in the first half, with Oscar's 13th-minute shot coming closest after it was pushed onto the post by Lindegaard following a run down the left side by the Brazilian.
Victor Moses fired wildly over the crossbar moments later, something Cleverley did later in the half, while Anderson almost converted a Phil Jones' cross with a header. Robin Van Persie also turned a Ryan Giggs's ball wide of Petr Cech's post in the 42nd minute.
"United were a little more relaxed after winning the title, I told my players that at half-time," Benitez said. "I tried to get them to increase the tempo."
Chelsea did, though the breakthrough did not come until Ramires burst through the centre after winning the ball from substitute Rooney, and the ball founds itself to Mata, whose low shot deflected off Phil Jones and continued into the goal via the far post.
Rafael was sent off two minutes after kicking out at Luiz as they battled for possession by the corner flag.
Luiz, who had elbowed his compatriot in the chest, was not punished and was clearly shown enjoying the situation on television replays.
Chelsea have knocked United out of both domestic cup competitions this season. They can add a league victory at Old Trafford to that, not that it was as vital as they would have hoped in August.
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