Real, who were stunned by third-division Alcoyano in the Copa del Rey on Wednesday, took the lead through a header by midfielder Casemiro.
Benzema added Madrid’s second of the game, his first of the night before Eden Hazard stroked in a third for the visitors.
A better performance from Alaves in the second half resulted in a goal scored by Joselu but Benzema made it 4-1 with a curled finish with about 20 minutes from time.
Watch the highlights of the match below
The victory ensured that Real Madrid moved to within four points of La Liga leaders Atletico Madrid, who have two games in hand.
Real boss Zinedine Zidane who tested positive for coronavirus was not on the sidelines for this game.
Other La Liga results
Saturday 23rd January
- SD Huesca 0-0 Villarreal
- Sevilla 3-0 Cadiz
- Real Sociedad 2-2 Real Betis
- Alaves 1-4 Real Madrid