Erik ten Hag's side entered the match knowing that a draw would be enough for them to guarantee their involvement in next season's Champions League with a game to spare.
The 20-time English champions were comfortably victorious on the night, though, and the result has moved them into third position, two points clear of fourth-placed Newcastle United ahead of the final matchday.
Casemiro and Anthony Martial scored in the first half for the Red Devils, before Bruno Fernandes, from the penalty spot, and the returning Marcus Rashford registered in the second 45 minutes; Joao Felix netted a late consolation for Chelsea, but it was too little, too late for Frank Lampard's side.
Liverpool's position in the Europa League has now been confirmed, while Chelsea remain down in 12th position, three points ahead of 14th-placed West Ham United.
Rashford was fit enough to return to the squad after a spell out with injury and illness, but the England international was only on the bench, with Ten Hag naming an unchanged side for the third game in a row following the back-to-back wins over Wolverhampton Wanderers and Bournemouth.
Chelsea's team, meanwhile, showed three changes to the side that started the loss to Manchester City last time out, with Carney Chukwuemeka, Mykhaylo Mudryk, and Noni Madueke coming in for Thiago Silva, Ruben Loftus-Cheek and Raheem Sterling.
At 23 years and 238 days, it was actually Chelsea's youngest ever average Premier League starting XI, with Lampard looking to give the club's fans something to cheer in Manchester.
The visitors had an opportunity of their own in the third minute, which came following a slip from Victor Lindelof, but Chukwuemeka's effort was always rising over the crossbar.
Chelsea then had a golden chance in the fourth minute when Lewis Hall broke down the left before delivering an excellent pass into Mudryk, but the January signing somehow missed the target from close range.
Man United instead made the breakthrough in the sixth minute, with the Brazil international heading a wonderful free kick from Christian Eriksen into the back of the net from close range; there was a check for a possible offside, and it was close, but the goal was ultimately given.
Fernandes almost gathered a Sancho pass in the ninth minute, which would have given him a clear strike on goal, but the ball just ran away from the Portugal international at the vital moment.
Antony sent one just wide of the Chelsea goal in the 13th minute, before Martial passed up another chance in the 19th minute, with his heavy touch inside the box following a clever Antony pass allowing Azpilicueta back to make the challenge.
There was a lengthy stoppage in the middle of the first period, with Antony staying down following a heavy challenge from Trevoh Chalobah, which led to the Brazilian leaving the field in tears on a stretcher, and Rashford entered the field as his replacement.
Chelsea had a golden chance to level in the 32nd minute when Hall found Havertz inside the Man United box, but the Germany international somehow headed wide of the post.
The Blues were on top in the period that followed, with Hall having a goal-bound strike blocked, while Havertz, Gallagher and Madueke were all seeing plenty of the ball in dangerous areas.
Gallagher sent one just wide of the target in the 44th minute, before the Englishman just missed the post from an even better position in first-half stoppage time.
Man United managed to double their advantage in the final stages of the first period, though, with Martial converting from close range after an excellent pass from Sancho, who had been found by Casemiro inside the Chelsea box.
Fernandes crashed one against the post in the 47th minute following smart work from Lindelof and then Sancho, with the home side looking to put the match beyond Chelsea.
David de Gea had to tip a low Mudryk strike wide of the post in the 50th minute, before Man United had two big chances to net a third, with Eriksen somehow failing to convert a low Tyrell Malacia cross from close range and Casemiro then whistling one just wide of the post.
De Gea made two smart saves just before the hour, with Hall being denied by the Spaniard, before he flew across his goal to keep out a deflected Mudryk effort.
The Man United goalkeeper, who has won the Premier League's Golden Glove this season, then kept out a header from Havertz, with Chelsea continuing to have their moments in the final third of the field.
The home side were awarded a penalty in the 72nd minute when Wesley Fofana kicked out at Fernandes inside the penalty box.
Fernandes stepped forward for Ten Hag's side and found the bottom corner with a composed finish to secure all three points for the English giants and a position in next season's Champions League.
Rashford whipped one just wide of the far post in the 77th minute, but the Englishman then got his name on the scoresheet shortly after, converting at the second time of asking after a poor pass from Fofana had put his team in trouble.
Alejandro Garnacho crashed one off the crossbar in the 84th minute, but the visitors managed to give their fans something to cheer in the final exchanges, with Felix brilliantly picking out the bottom corner with a low strike.
Garnacho, Rashford and Scott McTominay all came close for Man United late on, but the home team ultimately declared at four.
Chelsea have set a new club record of 16 defeats in a 38-game Premier League season, while they are guaranteed to finish in the bottom half of the Premier League for the first time in 27 years.
Lampard's side will finish their campaign at home to Newcastle on Sunday, while Man United will welcome Fulham to Old Trafford on the same afternoon before switching their attention to the FA Cup final against Manchester City on June 3.No Data Analysis info