Ronaldo scored his 300th LaLiga goals in the victory.
Benzema created the opportunity with a clever back-heel which allowed Ronaldo to spin in the area and drill home.
They are seven points from Atletico Madrid in second and with Diego Simeone's side facing a hard trip to Sevilla on Sunday, Real have the opportunity to put further pressure on their local rivals. That has led to calls for others like Francisco "Isco" Alarcon and Marco Asensio to take their place.
Ronaldo struck Real's third goal of the day and his 299th in La Liga in the 61st minute, meeting a cutback from in-form winger Lucas Vazquez first time and sending it under the reach of former Real goalkeeper Fernando Pacheco.More news: More Evidence That iPhone X Demand Is Underwhelming
The trio, supported by the incisive play of Lucas Vazquez, made the difference against an Alaves side that had been playing well over the last two months under new coach Abelardo Fernandez. Ronaldo's goals were his 27th and 28th of the season in all competitions and took his tally in La Liga to 14.
The much-maligned Frenchman also had a hand in Madrid's second goal, teeing to Gareth Bale after Alaves lost the ball nearly directly from the kick off. The most important thing is the atmosphere in the dressing room.
With Alaves giving as good as they got on the counter-attack - Alfonso Pedraza and Alexis both drew vital saves out of Keylor Navas in the first half - Madrid knew an 11th victory in their last 12 meetings with the Basque side was far from certain. Elsewhere, Celta Vigo gave their hopes of qualifying for the Europa League a boost as Iago Aspas scored in a 2-0 win over Eibar.
The goals were Aspas' 16th and Gomez's 13th in the league.
Relegation-threatened Las Palmas scraped a point from drawing with Leganes 0-0 to inch its way toward safety.