In-form Benzema linked up with Dani Carvajal to score his fourth goal in as many league games just after the half-hour mark, making it 50 matches in a row in which Madrid have netted.
Alaves wasted numerous good chances for an equaliser in the second half and it looked like the Madrid striker's goal would ultimately prove to be the winner.
But a late strike from Isco – whose future is a hot topic amid rumours of a shock move to Barca – and a header from Nacho sealed a fourth consecutive league win for Zinedine Zidane's men.
The hosts were short of top form in their first game after the international break, with Sergio Ramos, Marcelo, Keylor Navas and James Rodriguez all rested, while Casemiro was suspended.
Nonetheless, the win sees the league leaders move five points clear of Barca, who travel to play Granada later on Sunday.
Alaves, who had won three of their last four top-flight away games, remain 10th in the table, but have a Copa del Rey final to look forward to.
After Cristiano Ronaldo fired over inside the first minute, Madrid were forced into an early change with injured defender Raphael Varane replaced by Carvajal.
Alaves' Edgar Mendez shot straight at Kiko Casilla and then had an ambitious penalty claim rejected after going down under pressure from Danilo and Nacho.
Madrid upped the pressure as the first half progressed, but they did not test Fernando Pacheco until Ronaldo impressively beat Gaizka Toquero with clever skill down the left and forced the goalkeeper into action at his near post.
The breakthrough arrived in the 31st minute. Despite Alaves claiming Benzema was offside in the build-up, Madrid's attack was allowed to proceed with the scorer and Carvajal exchanging four passes down the right before the Frenchman fired a low left-footed effort into the bottom corner from 10 yards.
It was almost two for Madrid on the stroke of half-time when Danilo charged into the box and delivered a square pass that found Gareth Bale in his stride, but the Wales forward's effort trickled agonisingly wide.
Alaves should have levelled straight after the restart when Deyverson latched on to Theo Hernandez's shot and headed over a super opportunity from close range after Casilla's claims he had been fouled by Manu Garcia prior to the chance were ignored.
Ronaldo had a goal ruled out for offside at the other end, his powerful finish correctly disallowed having strayed beyond the last defender from Benzema's throughball.
Alaves were proving the more threatening side, another huge chance going begging when Edgar somehow missed the target with his volley when left completely unmarked by the Madrid defence from Zouhair Feddal's looping left-wing cross.
But a late flurry saw Madrid seal victory with a more flattering scoreline. With five minutes remaining, Isco collected Ronaldo's pass before taking one touch and sending his finish high past Pacheco from a tight angle.
Just three minutes later, a superb Bale free-kick crashed against the crossbar, with Nacho reacting quickly to head in the rebound from inside the six-yard box to send the home crowd home happy.
7 - Isco Alarcon has been involved in seven goals in his last six La Liga starts (five goals and two assists). Jewel. pic.twitter.com/iiTYYomS0H— OptaJose (@OptaJose) April 2, 2017
Key Opta Facts:
- Karim Benzema has scored against all the 31 sides he has faced in LaLiga (120 goals).
- Real Madrid are the first LaLiga team to score in 50 games in a row in all competitions.
- No other LaLiga defender has made more assists than Dani Carvajal this season in all competitions (eight – level with Marcelo).
- Real Madrid have scored in their last 40 LaLiga games, their best scoring run in the competition.