Hazard, who signed from Chelsea in June, lobbed Rui Silva at the end of the first half after Karim Benzema’s second-minute opener for the hosts.
Luka Modric added an excellent third in the second half, but Darwin Machis and Domingos Duarte responded for Granada.
James Rodriguez then scored late in stoppage time to ensure Real’s victory.
The result sees Real open up a four-point gap over second-placed Granada.
Third-placed Atletico Madrid travel to Real Valladolid on Sunday (15:00 BST), while fourth-placed Barcelona host Sevilla later that day.
Real avoid late collapse
With his side criticised following another below-par performance against Club Brugge in the Champions League on Tuesday, manager Zidane called on his side to show why they began the weekend top of La Liga as they welcomed their closest challengers, Granada, to the Bernabeu.
Benzema’s finish – his sixth in eight league games – from Gareth Bale’s sublime pass using the outside of his left foot provided the ideal start on Saturday, while Hazard’s delightful first goal for the club on the stroke of half-time ensured the scoreline reflected the hosts’ early dominance.
Real appeared to be coasting as Modric smashed in his side’s third from outside the area after 61 minutes, but in keeping with their season to date it was not to be so straightforward.
Goalkeeper Alphonse Areola, in for the ill Thibaut Courtois, made a mess of a back pass eight minutes later before bundling over Alvaro Vadillo – and Machis took his opportunity from the penalty spot.
Then, with 12 minutes remaining, Vadillo’s corner was flicked on by Victor Diaz at the near post for centre-back Duarte to ratchet up the tension in the Spanish capital.
Silva denied Benzema a second as Real pressed for a fourth, before Rodriguez’s strike on the break wrapped up a victory that half an hour previous seemed almost guaranteed.
Top and unbeaten after eight league matches, the pressure on Zidane appears to be lifting – domestically at least.