Olivier Giroud headed in the only goal of the game, as Chelsea defeated Liverpool 1-0 at Stamford Bridge on Sunday.
The Blues came into the game, needing a victory to keep their slim hopes of squeezing into the top four alive.
Although the visitors started the game strongly, causing problems through Sadio Mane, it was Chelsea who took the lead.
Victor Moses produced a fine cross with his left foot for Giroud to head past Loris Karius.
The win takes Antonio Conte’s men to 69 points, two behind Tottenham Hotspur who lost 1-0 to West Brom on Saturday, with two fixtures left.