Benzema diverted a Cristiano Ronaldo centre past goalkeeper Carlos Kameni in the 18th minute at the Rosaleda and Bale finished off a swift break, in which Ronaldo was also involved, seven minutes from time.
Former Malaga midfielder Isco was dismissed in the 86th minute and the hosts pulled a goal back in stoppage time when Roque Santa Cruz nodded past Iker Casillas.
Real have 33 points from 13 matches and the victory helped them surpass their previous best of 15 successive wins in all competitions set in 1960-61 and 2011-12.
Carlo Ancelotti’s men have won all their games since a 2-1 league defeat at home to champions Atletico Madrid in September.
“It’s always a very tough match here,” Real full back Marcelo told Spanish television.
“We managed to beat the record but with a lot of work and commitment from the team,” added the Brazil international. “Our main objective is to carry on winning each game.”
Barca can trim the deficit to two points at fourth-placed Valencia on Sunday when Atletico, third on 26 points, host promoted Deportivo La Coruna.
Qatar-owned Malaga, who are sixth, put up a fight against the European champions and after Benzema’s opener they came close to an equaliser two minutes before halftime when a long-range free kick by captain Duda clipped the top of the crossbar.
Real took control in the second period and Kameni, who earlier produced a brilliant point-blank save to deny Bale, had to race off his line to block an Isco shot in the 56th minute.
Santa Cruz headed a corner narrowly over in the 67th before Kameni conjured another stunning save when a defensive error gifted possession to Ronaldo in the centre of the penalty area.
The Portugal captain sent a low shot towards the corner but Kameni flung out an arm to palm the ball away.
Isco’s return to his home city ended badly when he received a second yellow card although he was given a rousing ovation by the Malaga fans as he trudged off the pitch.
“I think Madrid deserved the victory,” said Cameroon international Kameni. “We showed today that we deserve a lot of credit and we have achieved great things in the opening part of the season.”
Elsewhere, Celta Vigo missed a chance to climb above Malaga and draw level on 23 points with fifth-placed Sevilla when they lost 1-0 at home to Eibar, who moved up to 10th on 16 points.
Athletic Bilbao continued their revival after a poor start with a 2-1 win at Getafe that put them level on 18 points with eighth-placed Villarreal who visit Cordoba on Sunday.
Espanyol climbed to 11th, four points behind Villarreal and Bilbao, thanks to a 2-1 victory at home to 15th-placed Levante in teeming rain in Barcelona. (Reuters)