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.
What does it mean? 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.
Key Opta facts
- Real Madrid have won their last four LaLiga games - their best run in the competition since March 2018.
- Madrid faced just one shot on target against Alaves. It equals their lowest tally in a single game this season in all competitions (the same as against Sevilla and Getafe, all at Santiago Bernabeu in LaLiga).
- Karim Benzema has scored 10 goals in LaLiga this season. That is double the amount he scored in the last campaign (five).
- Mariano Diaz has scored his first goal for Madrid in LaLiga since December 10, 2016 against Deportivo Coruna.
- Alaves boss Abelardo Fernandez have just won one of his six games against Real Madrid as manager in LaLiga (D1 L4).
Madrid play the first of three forthcoming games against Barcelona in the Copa del Rey semi-final on Wednesday before facing Atletico, while Alaves will hope to return to winning ways when they take on Levante.