Two goals from Higuain and Hazard helped Chelsea thrash visitors Huddersfield after a humiliating 4-0 defeat away to Bournemouth.
New signing Higuain opened the score line for the Blues in the 16th minute following a reverse pass from N’Golo Kante.
Eden Hazard made it 2-0 for Chelsea before half time from the penalty spot after Cesar Azpilicueta was brought down by Elias Kachunga inside the box.
Eden Hazard’s goal is his first goal of the year and the league. He last scored in December.
In the 66th minute Hazard bagged his second and third for Chelsea after rounding goalkeeper Jonal Lossl and slotting it home.
Three minutes later Higuain scored his second and fourth for the Blues, curling a wonderful shot with the help of a deflection.
In the dying minutes of the match, Brazil defender David Luiz made it five after his powerful header was deflected into the net by Kachunga of Huddersfield.
The win for Chelsea takes them above Arsenal with 50 points and six points behind third placed Manchester City.
Huddersfield remain at the bottom of the table with 11 points, six points behind 19th placed Fulham.
In other results of the day, Tottenham scored a solitary goal against Newcastle to take them to second place, a point above third placed Manchester City.
Everton were thrashed three goals to one by visitors Wolverhampton. Wolves now sit 5 points ahead of Everton in 7th position behind Manchester United.
Southampton were held to a 1-1 draw away to Burnley as Crystal Palace thrashed struggling Fulham two goals to nil.