Bale opened the scoring with a powerful effort, the seventh consecutive La Liga game in which he has scored.
Guido Carrillo equalised with a penalty but Benzema then headed in a goal awarded by the video assistant referee.
He then blasted in a fine second – his fourth goal in two games – before Sergio Ramos added a penalty.
Benzema has now scored five goals in four games this season, with Bale scoring three. Ronaldo, meanwhile, has yet to score his first goal for Juventus after three Serie A matches – although his side has won all three games.
Former Chelsea goalkeeper Thibaut Courtous made his Real debut but had a quiet night, only facing three shots on target including the penalty by Southampton loanee Carrillo.
Julen Lopetegui’s Real are the only team to win their opening three La Liga games, although champions Barcelona can emulate them when they host Huesca on Sunday (17:30 BST).