With the victory, Chelsea set a club-record 12th successive Premier League victory while Hazard also earned his 50th Premier League goal
Pedro had given Chelsea the lead with a curled effort from 18 yards supplied by Cesc Fabregas’ 98th Premier League assist, before Hazard scored a penalty in the 49th minute after he was fouled by Simon Francis.
The Belgian became the sixth Chelsea player to reach 50 PL goals after Frank Lampard, Didier Drogba, Jimmy Floyd Hasselbaink, Gianfranco Zola and Eidur Gudjohnsen.
AFC Bournemouth were dangerous throughout and twice went close through Jack Wilshere and substitute Benik Afobe, but Antonio Conte’s men held firm and got a late third through Pedro’s deflected shot.