Madrid boosted its advantage to five points over Barcelona before the defending champions visit Granada later. Madrid also will have a game in hand.
Madrid dominated the first half and Benzema's opener in the 31st minute came from a one-two with Dani Carvajal, who put the ball back into the box for the striker to fire home.
But in its first match since a long international break, Zinedine Zidane's team faded in the second half and Alaves threatened to snatch a draw.
The win wasn't secure until the 85th when Francisco "Isco" Alarcon fired in a second goal from a pass by Cristiano Ronaldo. Defender Nacho Fernandez then headed in the rebound after Gareth Bale's free kick came off the bar.
Edgar Mendez had the best shot for Alaves in the 60th when he was left all alone in the six-yard box, only for the forward to drive the ball back past the far post.
Deyverson and Manu Garcia also went close with headers for the Basque team that is outperforming its small budget this season and faces Barcelona in the Copa del Rey final. Alaves remained in 10th place.
SEVILLA 0, SPORTING GIJON 0
Sevilla's slump continued after a fourth consecutive round without a win. That cost it the chance to reclaim third place from Atletico Madrid.
Jorge Sampaoli's side had enjoyed an excellent season but, in the last month, it has been eliminated from the Champions League's Round of 16 and seen its Liga title chances fading away.