Chelsea took the lead in the 13th minute in west London when Marcos Alonso headed home from close range.
Hazard then added a second goal shortly after the break with a superb solo goal to put Chelsea 2-0 up.
Substitute Cesc Fabregas then added a third for the hosts, before Olivier Giroud netted a late consolation for the Gunners.
Hazard was in superb form against the Gunners and was named man of the match for his impressive display.
And former Manchester United defender Neville heaped praise on the Belgian playmaker after the game.
Speaking to Sky Sports after the game, Neville said: “Eden Hazard is a shining light.
“He’s a truly world class player on his day.
“He was brilliant against Arsenal.”
Title favourites and table toppers Chelsea now turn their attentions towards their next Premier League game – a trip to Turf Moor to take on Burnley next weekend.
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