Barca had laid down a marker with a 1-0 victory at Sporting Gijon earlier on Saturday but Manuel Pellegrini's Real shrugged off the absence of the suspended Cristiano Ronaldo and injured top scorer Gonzalo Higuain to keep pace with the champions.
Real had not won at Deportivo's Riazor stadium in 19 years but Benzema went close early on for the dominant visitors before a defensive howler gifted them the lead in the 13th minute.
Defender Laure Sanabria attempted to head the ball clear but could only divert it to the unmarked Esteban Granero who sent a powerful header past goalkeeper Daniel Aranzubia.
A piece of brilliance from mercurial midfielder Guti created Real's second for Benzema five minutes before the break.
Kaka raced clear on the left and put Guti through on goal but instead of shooting he backheeled the ball to the France striker, who swept home with Aranzubia stranded.
Riki netted an 87th-minute penalty for Depor after Sergio Ramos had brought the striker down in the penalty area before Alvaro Arbeloa set Benzema up for his second in added time.
QUICK FREE-KICK
Pedro's clinical finish had earlier fired Barca to victory at a rain-lashed Molinon stadium in Gijon.
Barca took control from the start, with Xavi and Andres Iniesta providing the creative spark in midfield and Lionel Messi, Zlatan Ibrahimovic and Pedro, starting on the left instead of Thierry Henry, threatening up front.
Gijon battled bravely to keep the visitors at bay but were caught out on the half-hour when Messi tapped a quick freekick to Iniesta.
With the home defence on their heels, the Spain midfielder released Pedro who sprinted through the centre to finish coolly past goalkeeper Juan Pablo with a low, left-foot strike.
Barca had scored 12 goals without reply in their previous three league games and carved out a host of chances in the second half.
Pedro blasted over in the 73rd minute after good work from Messi and then somehow allowed the ball to be hooked off his toes with the goal at his mercy a minute later.
Barcelona coach Pep Guardiola said he was pleased at the way his side had controlled the match but was unhappy that so many chances to make the game safe had gone begging.
"There's still an eternity until the end of the season," he told a news conference. "Every match is a battle because all our opponents are fighting for something."
In Saturday's earlier match, striker Luis Garcia smashed in a loose ball in the 58th minute to give Espanyol a 1-0 home win over Athletic Bilbao and lift the Barcelona-based club further away from the relegation places.
