City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat
The Belgian wizard tormented West Ham throughout at Stamford Bridge and scored both goals to move Chelsea above Arsenal and Tottenham Hotspur in the race for a top-four finish.
Hazard danced through West Ham's defence in the 24th minute to put Maurizio Sarri's side in front and Gonzalo Higuain should have buried the visitors before halftime.
West Ham improved after the break and Manuel Lanzini and Felipe Anderson both had good chances to equalise but Hazard sealed the points in the 90th minute with a clinical finish.
A third successive victory means Chelsea have 66 points from 33 games, while Tottenham and Arsenal have 64 and 63 respectively having played a game less.
West Ham are 11th with 42 points from 33 games.