Chelsea had to come from behind after the visitors went ahead on 16 minutes when Sol Bamba finished off a headed pass from Sean Morrison.
The Blues levelled in the 37th minute following a brilliant passing move which culminated in Hazard finishing from Olivier Giroud's lay-off.
Hazard struck again a minute before half-time when he latched on to another Giroud pass.
Hazard completed his treble with an 80th-minute penalty following a foul by Bamba on Willian.
The Brazilian substitute added a fourth to keep Chelsea level at the top with Liverpool.
Chelsea: 23 Sep v West Ham (A)
Cardiff: 22 Sep v Man City (H)