Hazard, who has been strongly linked with a move to Real Madrid this summer, evaded five players during a stunning run, before the Belgium forward calmly beat keeper Lukasz Fabianski.
He added a late second goal to cap a magnificent individual performance in an entertaining game.
Gonzalo Higuain hit a post, while Hazard was denied a penalty after what looked like a foul by Marko Arnautovic, with Argentine midfielder Manuel Lanzini going closest for West Ham with a shot which was beaten away by Kepa Arrizabalaga.
Chelsea, who can still qualify for next season’s Champions League by winning the Europa League, are three points ahead of fifth-placed Arsenal, who have a game in hand, after a third successive league win.
The Hammers remain 11th after a third defeat in four league games.
On a day fresh reports circulated about Hazard moving to Spain’s capital, the 28-year-old produced a breathless performance to show why he is one of Europe’s best forwards.
He was outstanding from start to finish against the West Ham, inspiring his side to an 11th top-flight win at Stamford Bridge this season.
In the space of a few first-half minutes, Hazard scored his 15th – and arguably best – league goal of the season, produced a wonderful pass which saw Higuain hit a post, and appeared to be fouled by Austria forward Arnautovic inside West Ham’s penalty area.
To the bewilderment of Hazard and Chelsea, referee Chris Kavanagh waved away the home side’s appeals.
Hazard’s opening goal was beautiful, the Chelsea player receiving the ball just inside the Hammers’ half before using both feet during an unstoppable run which ended with the ball in the net.
His second, a powerful low finish, sealed a deserved win for Maurizio Sarri’s side.
Hazard’s contract expires in the summer of 2020 and Blues fans will hope the club do not cash in on their prize asset after Real Madrid boss Zinedine Zidane admitted he has “always appreciated” the Chelsea player.
With the London club hit with a Fifa transfer ban preventing them from signing players until the end of January 2020, Chelsea would have to wait to spend any money if they did decide to sell Hazard.
