Real Madrid boss Zinedine Zidane made five changes to the team that started against Athletic Bilbao before the international break, with Danilo, Raphael Varane and Pepe coming into the back four, while there was a change between the sticks as Kiko Casilla replaced under-fire stopper Keylor Navas.
As for Alaves, on-loan Atletico Madrid defender Theo Hernandez was passed fit after overcoming a muscular problem, while Edgar Mendez and Gaizka Toquero both came into the team following the 1-0 win over Real Sociedad last time out.
Ronaldo sent an early warning to Alaves inside the first 60 seconds after collecting a loose ball in a forward position and firing towards goal, but the number seven's effort was always rising over the crossbar.
Varane, on his return from a hamstring problem, only lasted 11 minutes at the Bernabeu as the Frenchman pulled up with what seemed to be a reoccurrence of his previous injury, which will be a worry for Zidane entering a busy April.
Benzema was next to try his luck for the home side after finding a yard of space outside the Alaves box in the 16th minute, but the Frenchman's effort was too high, before Bale sent a free kick wide of the post two minutes later.
Dani Carvajal and Isco also missed the target with efforts in the opening 25 minutes of action, where Real Madrid had plenty of the ball without really threatening to make the breakthrough. The home side's first shot on target came from Ronaldo in the 27th minute, although Fernando Pacheco was down to make a comfortable save.
Real Madrid took the lead in the 31st minute, however, when Carvajal broke down the right before delivering a low cross into Benzema, who found the corner of the net with a composed finish.
Deyverson had a half-chance to level the scores in the latter stages of the first period when he met a cross from Ibai Gomez, but the striker's header was wide of the far post, before Bale swept a low Danilo cross just wide as Real Madrid entered the half-time interval with a one-goal lead.
Alaves had a golden chance to level the scores early in the second period when Hernandez bounced a cross into Deyverson after Casilla had failed to collect a high ball, but the striker's header was somehow over the crossbar.
Ronaldo looked to have doubled Real Madrid's lead in the 54th minute after finding the back of the net with a composed finish from inside the Alaves box, but the offside flag prevented the Portugal captain from getting his name on the scoresheet.
Deyverson had another brilliant opportunity for the visitors just before the hour after being picked out by Toquero inside the Real Madrid box, but the number 20 again sent his header wide of Casilla's post, before Mendez missed an even better chance for the Basque outfit on the hour mark.
Alaves continued to threaten as the second period developed, with Manu Garcia heading wide of the post 20 minutes from time during a spell where Real Madrid were unable to threaten down the other end of the field.
Mateo Kovacic replaced Luka Modric as Zidane freshened his midfield for the final part of the match, but the pattern of the contest did not change as Alaves continued to look the team more likely to add to Benzema's first-half strike.
Ronaldo had a half-chance in the 77th minute after smart work from Benzema released the Portuguese, but his scuffed effort moved wide of the post as one goal continued to separate the two teams in the Spanish capital.
Lucas Vazquez replaced Benzema in the 81st minute as Zidane made his third and final change, and the substitution was a mark of respect to an Alaves side that deserved more on the afternoon.
Bale hit the post for the home side in the 83rd minute after stretching to meet a deep cross from Carvajal, but Real Madrid made sure of all the points in the 85th minute when Isco found the back of the net with a brilliant finish from a narrow angle.
Two then became three in the 88th minute when Nacho headed home from close range after a thumping free kick from Bale had rattled against the away side's crossbar.
Next up for Real Madrid is a trip to Leganes on Wednesday, while Alaves will look to return to winning ways when they host basement side Osasuna on the same night.