Eden Hazard’s second-half strike was enough to give Chelsea a victory their dominance deserved.
The Blues controlled the first period without finding the breakthrough, but Hazard crashed in the winner six minutes into the second period after good work by Alvaro Morata.
Bournemouth rarely threatened an equaliser despite upping their tempo and urgency following the Belgian’s composed finish.
Steve Cook came the closest, shooting straight at Thibaut Courtois from 15 yards in injury time.
Chelsea, who climb back up to fourth in the Premier League table, just a point behind Tottenham who lost to Manchester United, should have won by a greater margin.
Morata went close on three occasions before the break.
His best chance saw him played in by Hazard after a shocking clearance by former team-mate Asmir Begovic, but the Spaniard shot narrowly wide of the near post.
He did find the back of the net from close range after Begovic failed to hold a David Luiz shot, but Cesar Azpilicueta was offside as he challenged the keeper.
Morata also had a shot tipped wide, but he did make a decisive contribution after the interval when he withstood a couple of strong challenges and found Hazard, who netted after racing in from the left.
Fabregas could have added a second in the final 10 minutes, shooting over the bar from a tight angle following a swift break and Chelsea held on despite the late scare when Cook went close.
Chelsea: Courtois; Azpilicueta, Luiz, Rudiger; Zappacosta, Bakayoko, Fabregas, Alonso; Pedro (Drinkwater 79), Hazard (Willian 85), Morata (Batshuyai 79).
Subs not used: Caballero, Cahill, Christensen, Ampadu.
This post was last modified on 28/10/2017