After Thursday night's win, Erik ten Hag's side are now guaranteed to finish at least fourth in the Premier League and can therefore look forward to joining Arsenal, Manchester City and Newcastle United in Europe's elite club competition in the 2023/24 season.
Carlos Casemiro gave United the perfect start with a header from a Christian Eriksen set-piece after just six minutes. While the visitors provided a threat in the first half, United laid another blow as Anthony Martial doubled the lead deep into stoppage time.
United came out strongly again after the interval, dominating the play as they steamed ahead with two more goals later in the half.
Bruno Fernandes was brought down by Wesley Fofana in the box, and the Portuguese converted the resulting penalty in the 73rd minute before teeing up Marcus Rashford four minutes later.
A late consolation effort from Joao Felix in the 89 minutes could not uplift Chelsea's hope as United sealed the win and confirmed their Champions League qualification for the 2023/24 campaign.
The win means United moved into third spot in the table, two points ahead of Newcastle, with one game still to play.
The 2023/24 UEFA Champions League group stage will involve 32 clubs, with 24 qualifying automatically by virtue of their domestic league placing.
The UEFA Champions League holders and previous season's UEFA Europa League winners are both also guaranteed a spot, with the final six slots determined via the play-offs.
Also Read | Ashes series: Jimmy Pierson to join Australia squad as cover for Inglis after first Test
Also Read | La Liga: Osasuna move into European places after beating Athletic Club