Los Blancos have now won two and drawn two of their four league matches at the start of the 2019-20 campaign, with the latest victory seeing them move behind Atletico Madrid in the table.
Madrid had a half-chance in the second minute when Benzema found space in a dangerous position before attempting to pick out the bottom corner, but it was a comfortable save for the Levante goalkeeper.
Los Blancos enjoyed a lot of the ball in the opening exchanges, but Levante were causing problems on the break with the movement of on-loan Madrid forward Borja Mayoral, who was allowed to play against his parent club.
Toni Kroos struck wide of the goal in the 13th minute as another half-chance came and went, before the midfielder had a goal-bound strike deflected over the crossbar four minutes later.
Benzema was next to come close in the 22nd minute with a rasping strike towards goal, but Aitor Fernandez was on hand to make another smart save for the visitors.
The French forward was not to be denied, though, and handed the home side the lead in the 25th minute when he headed an excellent Dani Carvajal cross into the back of the net from close range.
Benzema then registered his second in the 31st minute when he swept the ball into the bottom corner after being fed by James Rodriguez inside the Levante box.
Madrid were absolutely rampant as they went forward in search of more goals, and a third arrived five minutes before the interval when Casemiro slotted into the back of the net from close range after being found by fellow Brazil international Vinicius Junior.
It was a dominant first-half performance from Zidane's side, who had 12 attempts - seven of which were on target - to Levante's two, with the visitors failing to test Thibaut Courtois in the opening half of action.
Levante were on the scoresheet early in the second half, however, when Mayoral turned a low Carlos Clerc cross into the bottom corner before refusing to celebrate against the club that pay his wages.
Benzema came close to scoring a fourth for Madrid just before the hour, but the striker saw his low strike come off the post before Hazard entered the field for his competitive debut moments later.
Los Blancos thought that they had scored a fourth in the 62nd minute when Vinicius found the back of the net from close range, but the effort was chalked off due to an offside call, which was confirmed by VAR.
Hazard had been criticised for being overweight during a disappointing pre-season, but the Belgium international had a spring in his step at the Bernabeu as he caused Levante problems down the left.
Fernandez had to make a smart save to prevent Vinicius from registering 20 minutes from time, and Levante actually scored a second in the 75th minute when Gonzalo Melero headed home at the far post.
Levante threatened to make it an uncomfortable conclusion for the capital giants, and there was a huge chance for a leveller late on when Mayoral headed a brilliant Jose Luis Morales delivery towards goal, only for Courtois to make a brilliant save as the home side earned the win.
Next up for Madrid is a trip to Paris Saint-Germain in the Champions League on Wednesday before visiting Sevilla in the league next weekend. Levante, meanwhile, will attempt to return to winning ways when they host Eibar on September 21.
REAL MADRID (4-3-3): Courtois; Carvajal, Varane, Ramos (Militao 61'), Marcelo; Casemiro (Hazard 60'), Kroos, James; Vinicius, Benzema (Jovic 83'), Lucas
LEVANTE (5-4-1): Fernandez; Miramon, Vezo, Duarte (Melero 68'), Postigo, Clerc; Rochina (Roger 68'), Vukcevic (Bardhi 56'), Campana, Morales; Mayoral body check tags ::