Chelsea returned to winning ways with a much-needed 5-0 victory over Huddersfield.
Higuain opened the scoring after 16 minutes with his first goal for Chelsea, who came under scrutiny after they were thrashed 4-0 by Bournemouth on Wednesday.
Hazard made it 2-0 with a penalty in first-half injury-time and then added the third in the 66th minute.
Chelsea and Maurizio Sarri had faced some tough questions after their worst Premier League defeat in 23 years in midweek, but they made an encouraging start against Huddersfield as Ross Barkley flashed a shot wide and Hazard forced Jonas Lossl into a diving save.
Huddersfield had the best chance of the opening 15 minutes, though, as Mooy headed over the bar from Chris Lowe’s cross.
Chelsea took the lead in the 16th minute when N’Golo Kante slipped a well-disguised pass into the box for Higuain, who fired past Lossl at the near post.
Higuain then went close to a second as he poked wide from Marcos Alonso’s cross.
Huddersfield threatened on the break when Philip Billing saw a shot blocked, but Chelsea added to their lead late in the half as Hazard converted from the penalty spot after Cesar Azpilicueta had been fouled right on the edge of the box.
The visitors were denied a penalty of their own early in the second half when Elias Kachunga went down in the box under a challenge from Andreas Christensen.
Two goals in three minutes then put Chelsea in firm control, with Hazard finishing after rounding Lossl and Higuain curling in a shot from 20 yards with the aid of a deflection.
Luiz headed in from a corner in the 86th minute to round off the win.
Man of the match – Eden Hazard
After reportedly being singled out for criticism by Sarri after Chelsea’s defeat to Bournemouth, Hazard responded with a fabulous individual display. He was always a threat on the ball, even managing to stay on his feet after two players tried to bring him down in the second half.
Chelsea face a trip to Manchester City in the Premier League next Sunday, Huddersfield host Arsenal on Saturday.