Making his first league appearance of the season, the Belgium star opened the scoring in brilliant fashion before Karim Benzema doubled the lead at Estadio Alfredo Di Stefano.
Federico Valverde scored the third after some fine interplay between Benzema and Hazard, who looked sharp throughout his hour on the pitch, before David Ferreiro's consolation.
Much of the pre-game talk had centred on Benzema and a recording of him appearing to tell Ferland Mendy not to pass to Vinicius Junior during the Champions League draw with Borussia Monchengladbach, and the striker should have scored his side's fourth when teed up by substitute Vinicius in what would have capped an improved Madrid display.
Benzema eventually got his second in the 90th minute, nodding in from Rodrygo's header across goal.
An obstinate Huesca kept Madrid at bay for much of the first half, although Sergio Ramos – making his 500th appearance in LaLiga – saw a header saved by Andres Fernandez.
The breakthrough came 40 minutes, as Hazard produced a moment of true brilliance too rarely seen in a Madrid shirt, rolling away from Kelechi Nwakali's challenge and blasting a left-footed shot beyond Fernandez from nearly 30 yards out.
Benzema doubled the lead just before the interval, chesting down Lucas Vazquez's deep cross before drilling a finish into the bottom-right corner.
Huesca started the second positively but the threat of a comeback was quashed 53 minutes in. After Hazard and Benzema had combined superbly down the left, the latter crossed for Valverde to take a touch and hammer home from 12 yards.
Benzema and Isco missed chances for a fourth before Ferreiro scored a consolation, steering a finish past Thibaut Courtois from Rafa Mir's cross, but Benzema had the final word when he turned in Rodrygo's header from point-blank range.
What does it mean? Hazard looks sharp again as Madrid return to top
The victory moved Madrid back to the summit of LaLiga, two points clear of Real Sociedad after seven games each.
It also marked an impressive return to form for Hazard and Zinedine Zidane's side as a whole, as they once again followed up a disappointing performance in Europe with a much-improved domestic display.
Huesca, one of just two sides without a LaLiga win this season, are 18th after eight games.
Hazard levels rising
This was not a virtuoso Hazard performance: he created zero chances for team-mates, produced no crosses and only had one shot on target.
However, that solitary strike earned him his first goal in 392 days and seemed to breathe some life into his link-up with Benzema. Zidane will be encouraged.
Auxiliary right-back Lucas Vazquez was taken off after 52 minutes and did not seem to be wholly comfortable. Given injuries to Dani Carvajal and Nacho, any further concerns in that position will be most unwelcome to Zidane.
Madrid host Inter in the Champions League on Tuesday before next Sunday's visit to Mestalla to meet Valencia. Huesca have a week off until they host Eibar.