Under coach Jose Mourinho, the France international has started most games on the bench, scoring only one league goal before Sunday, and the club have said they are looking for another striker to replace the injured Gonzalo Higuain.
Real struggled to create chances against a gritty Mallorca, who held them to a 0-0 draw on the opening day of the season, and looked in danger of dropping points for a second successive game until Benzema netted in the 61st minute.
The former Olympique Lyon forward picked up a pass on the edge of the penalty area, created space for himself and sent a low shot past Mallorca's Israel goalkeeper Dudu Aouate.
Barca have 55 points from 20 matches, Real have 51 in second and Villarreal are third on 42 after a double from Italy striker Giuseppe Rossi gave them a 2-1 comeback win over visiting Real Sociedad in Sunday's late kick-off.
Valencia are two points further back thanks to Saturday's 4-3 home win against nine-man Malaga.
Real Madrid's week had been overshadowed by media reports of a rift between Mourinho and club director general Jorge Valdano and some fans unfurled a banner with a message of support for their Portuguese coach.
With an eye on Wednesday's King's Cup semi-final first leg at holders Sevilla, Mourinho initially rested midfielders Xabi Alonso and Mesut Ozil and Michael Laudrup's well-drilled Mallorca side had the best of the early exchanges.
Real survived a scare at the death when Casillas saved Pierre Webo's close-range strike.
"I decided to make some changes because we are playing another important match (in the Cup) on Wednesday," Mourinho told a news conference.
"Getting to half-time at 0-0 was a very good result for us because we knew we were going to make changes," the Portuguese added. "The changes had their effect and we got a very hard and very important victory."
In Sunday's earlier games, Atletico Madrid's hopes of a Champions League place next season were dealt a blow when they lost 1-0 at struggling Sporting Gijon.
