Madrid was in desperate need of a victory after a Supercopa de Espana reverse to Athletic Bilbao and a shock Copa del Rey defeat to lower-tier Alcoyano piled the pressure on Zinedine Zidane, who was absent on Sunday (AEDT) after testing positive to COVID-19.
Atletico Madrid's late victory at Eibar on Friday (AEDT) had moved it seven points clear in the title race, although Los Blancos never looked in danger of failing to win on the road in LaLiga for a third successive game, Benzema and Hazard putting them in control after Casemiro's opener.
Joselu's fifth league goal against Madrid gave Alaves hope, but Benzema's second meant the visitors had little trouble seeing out just their second win in 2021.
Benzema seemed set to open the scoring when he latched onto Luka Modric's lofted pass, only to be denied first by Fernando Pacheco and then a deflection onto the right-hand upright.
Madrid made the resulting corner count, though, with Casemiro rising high to head home from Toni Kroos' outswinger.
Madrid’s second goal should have followed in the 22nd minute, yet Ferland Mendy failed to tee up Benzema for a simple finish.
Benzema had his goal 19 minutes later, sensationally picking out the top of the net with a wonderful, dipping effort from just inside the penalty box.
Having curled wide earlier on, Hazard made it three on the stroke of half-time with a delicate finish over the on-rushing Pacheco.
Madrid is Joselu's favourite LaLiga opponent and the forward netted again when facing the capital club, this time sending a brilliant header beyond Thibaut Courtois.
Alaves's comeback hopes were quashed with 20 minutes remaining, however, when Benzema cut in from the left to thump home and settle the contest.