Half-time: Bournemouth 1 Chelsea 2
Goals from Pedro and Eden Hazard put Chelsea in command at the Vitality Stadium before Tommy Elphick pulled one back for the hosts.
Barely three minutes had been played when the Blues went in front. A swift counter ended with Cesc Fabregas finding fellow Spaniard Pedro, who finished coolly past Bournemouth keeper Artur Boruc.
The Cherries, seeking to do the double over Chelsea after December’s win at Stamford Bridge, forced a couple of saves from Blues keeper Asmir Begovic, starting in place of the suspended Thibaut Courtois.
The Bosnian first denied Lewis Grabban at his near post and then held Josh King’s header.
Just as Bournemouth looked the team more likely to score, Chelsea conjured a second goal.
Hazard, back in the team for the first time since 9 March, drifted in from the left and fired in a low shot from the edge of the box which beat Boruc.
But Bournemouth immediately cut the lead in half when skipper Elphick, up from centre-half, guided in a header from a corner.
Begovic had to make a very good save from Junior Stanislas to prevent an equaliser as Guus Hiddink;s side led at the end of an open first half.
Chelsea: Begovic; Azpilicueta, Ivanovic, Mikel, Baba; Matic, Fabregas; Pedro, Willian, Hazard; Diego Costa.
Subs: Amelia, Miazga, Loftus-Cheek, Kenedy, Traore, Pato, Falcao.