Three days on from the embarrassing Copa del Rey loss to third-tier Alcoyano, Real scored three times in the first half at Mendizorroza, with Casemiro heading in the opener in the 15th minute.
Benzema added a fierce 41st-minute strike having been teed up by Eden Hazard, who then slotted in the third moments later.
Joselu reduced the deficit with a header just prior to the hour mark before Benzema struck his second in the 70th minute.
It was a first win in four games in all competitions for Real, whose boss Zinedine Zidane was absent from the contest after testing positive for coronavirus.
The result leaves the second-placed defending champions – now unbeaten in nine league outings – four points behind Atletico Madrid, having played two games more. Atletico are in action on Sunday, hosting Valencia.
Alaves made a bright start, with Joselu and Martin Aguirregabiria seeing efforts go off target before Benzema had a shot blocked at the other end.
Hazard went close with a shot around the half-hour, then produced a clever flick to set up Benzema's goal towards the end of the half.
The Belgian subsequently netted the third soon after, latching on to Kroos' pass and sending a finish beyond Pacheco.
Alaves made another strong start after the break and after Joselu had brought a good save out of Thibaut Courtois, he beat him with a header from Lucas Perez's corner.
Real, though, restored their three-goal cushion as Benzema cut into the box from the left and fired a low strike into the corner of the net.