Goals from Olivier Giroud, Willian and Ross Barkley took Chelsea back into the top four,
Giroud’s tidy finish and Willian’s penalty – the Brazilian’s sixth goal in his past seven matches and his ninth Premier League goal of the season – put the Blues in control by the interval.
Barkley capped the victory by slotting home in injury time after being set up by Cesar Azpilicueta.
Chelsea started the game under some pressure, with Manchester United having moved above them into fourth place after beating Bournemouth 5-2 earlier in the day.
Frank Lampard’s side, beaten at West Ham in midweek, responded strongly – and moved to within one point of third-placed Leicester.
A neat build-up led to Chelsea going ahead on 26 minutes.
Barkley collected Mason Mount’s pass and slipped the ball through to Giroud, who fired into the far corner of the net.
And Willian tucked away the resulting spot-kick after Etienne Capoue’s clumsy foul on Christian Pulisic a couple of minutes before half-time.
Substitute Ruben Loftus-Cheek had a late chance to make it 3-0 but misdirected his header over the bar from Reece James’ right-wing cross.
But Barkley made no mistake after Azpilicueta cut the ball back for him from the left.
Chelsea: Kepa, James, Christensen, Zouma, Azpilicueta, Kante (Gilmour 77), Mount (Loftus-Cheek 76), Barkley, Willian (Hudson-Odoi 76), Pulisic, Giroud (Abraham 76).
Subs not used: Caballero, Rudiger, Alonso, Jorginho, Pedro.