The French striker knocked a cross from Spanish left back Sergio Reguilon into the net from close range on the half hour mark, breaking the deadlock against an organised Alaves side who beat Real 1-0 earlier in the season at Mendizorrotza.
Santiago Solari's side looked comfortable without hitting top gear although they did not seal the victory until in-form Brazilian Vinicius Jr. tapped into the net in the 80th minute to score his first goal in La Liga.
Spain international Alvaro Odriozola had a goal ruled out for offside but substitute Mariano Diaz completed the scoring with a diving header.
Real, the only top-three side in La Liga to win this weekend, moved on to 42 points, two behind second-placed Atletico Madrid, who lost 1-0 at Real Betis, and eight adrift of Barca who drew 2-2 at home to Valencia.