The Frenchman struck after 30 minutes of a one-sided contest at Santiago Bernabeu where Gareth Bale made his first start overcoming a calf injury but Vinicius Junior stole the show, including scoring his side's second.
It was the 18-year-old who unlocked the Alaves defence with a killer pass in the build-up to Benzema's opener, and he converted Marco Asensio's low cross to double Madrid's advantage 10 minutes from time.
Substitute Mariano Diaz added a late third as Madrid moved to within two points of second-placed Atletico - who lost 1-0 away at Real Betis earlier in the day - in the table after a fourth consecutive win in LaLiga.
Guillermo Maripan's error almost allowed Dani Ceballos to open the scoring after three minutes but his shot deflected over the bar, while Benzema curled an effort narrowly wide from just inside the box moments later.
Vinicius slalomed through the Alaves defence before stinging the palms of Fernando Pacheco with a shot from 15 yards before playing a key role in the first goal.
The Brazilian teenager had the vision to see Sergio Reguilon's run and played him in behind the Alaves defence, with the defender sending over a low cross that Benzema side-footed into the net.
Ruben Duarte volleyed a rare Alaves chance wide from an acute angle at the start of the second half before Bale tested Pacheco with a low drive at the other end.
Santiago Solari replaced Bale and Benzema with Mariano and Asensio in the final half-hour and the latter's centre bounced through the Alaves box to the feet of Vinicius, who calmly provided the finish.
Alvaro Odriozola was denied a goal by an offside decision but did set up Mariano in additional time, the forward's firm header wrapping up a thoroughly convincing win for the hosts in the Spanish capital.
Second place in sight
After a tumultuous start to the season, Madrid have worked their way back into contention for a top-two finish and are now within striking distance of Atletico, who they play next in the league. Catching Barcelona - who are eight points clear of Solari's side - may be a tall order, but they will be focused on making sure they finish above their neighbours.
Vinicius growing in confidence
The hefty fee - reportedly €45million - Real Madrid spent to bring Vinicius to Spain last year looks like a bargain after the young forward put in a performance full of maturity and poise.
Fit-again Bale short of form
While Vinicius and Benzema zipped around the pitch, Bale looked rusty on his first start since January 3. The Wales international needs to hit form quickly with key games, both at home and in Europe, looming on the horizon.
