- Casemiro (6')
- Anthony Martial (45'+6')
- Bruno Fernandes (73' Pen)
- Marcus Rashford (78')
- João Félix (89')
Casemiro, Anthony Martial, Bruno Fernandes (penalty) and Marcus Rashford scored for United, who needed a point from their final two league games to officially end Liverpool's fading hopes of securing a spot in Europe's premier club competition.
"It's important; this club belongs in the Champions League," manager Erik ten Hag told Sky Sports. "But it's not easy in the Premier League. It's a tough competition, so it's a massive performance when you get this done."
Three-time European champions United, who failed to qualify for the Champions League last season, are third on 72 points with one game remaining, six points clear of fifth-place Liverpool.
Fourth-place Newcastle secured a spot among Europe's elite following a goalless draw against Leicester City on Monday. Chelsea, who have struggled all season, are 12th with 43 points.
United, who cap their Premier League season on Sunday by hosting 10th-placed Fulham, won the Carabao Cup in February and will be aiming to complete a domestic double when they face rivals Manchester City in the FA Cup final June 3.
"[The season has been] decent, it's not perfect because we want more," Fernandes said. "But for what we did this season, I think it's great. Won one trophy, we get to the top four -- that was our goal after we saw we couldn't go for the Premier League [title].
"Now it's about finish the league well and go to the FA Cup and win."
Ten Hag's side are unbeaten in Premier League action at Old Trafford for 17 games, going back to the opening weekend of the season.
"They know how important they are for us," Fernandes said of the home supporters. "You could see during the season how important it was in many games, so we just appreciate all the effort."
Casemiro scored in the sixth minute with a close-range header off a long free kick. The Brazilian midfielder helped set up Martial's goal just before half-time with a no-look chip into the path of Jadon Sancho. Martial was there to slot the ball into the empty net.
Interim manager Frank Lampard's Chelsea side collapsed in the dying minutes. After Fernandes had made it 3-0 with a penalty in the 73rd minute, Rashford returned from a two-game absence to score his 30th goal of the season in all competitions, cutting the ball around keeper Kepa Arrizabalaga.
Despite the jubilation of clinching a spot in the top four, a first-half injury to winger Antony as well as Luke Shaw will be a concern for Ten Hag ahead of United's match with Man City. The Red Devils are already without Lisandro Martinez and Marcel Sabitzer for that match.
Joao Felix pulled one back for the visitors in the 89th minute, but the game was as far out of reach as their season, with Chelsea set to finish in the bottom half of the Premier League for the first time since 1995-96.
- Stuart Attwell
|Brighton & Hove Albion||5||4||0||1||+8||12|
|West Ham United||5||3||1||1||+3||10|