The victory gave the nine-times winners an unbeatable 3-0 lead in the best-of-five tie and set up a last-eight clash against champions Spain or Switzerland in July.
Depleted Spain, missing injury casualties Rafael Nadal, Fernando Verdasco and Juan Carlos Ferrero, opened a 2-1 lead over the Swiss at the Plaza de Toros de la Ribera in Logrono when Tommy Robredo and Marcel Granollers dispatched Stanislas Wawrinka and Yves Allegro in four sets.
The tie now hinges on Sunday's reverse singles rubbers, with David Ferrer due to play Wawrinka (1100 GMT) and Nicolas Almagro facing Marco Chiudinelli.
"It was very important to get this second point for Spain and it will make our work tomorrow a little bit easier," Granollers said in a television interview.
The Swiss, without unavailable world number one Roger Federer, are bidding to become the first team to beat the Spanish in 19 home ties stretching back to a defeat by Brazil in 1999. Spain also won the title in 2000, 2004 and 2008.
French captain Guy Forget was pleased with the first Davis Cup outing for Llodra and Benneteau, who survived a third-set wobble to come through 6-1, 6-4, 1-6, 7-5.
"I'm very satisfied with the way they started the match," Forget said in a television interview.
"They were a bit shaky in the third set but they came back together in the fourth. We knew it would be a close doubles but we wanted to win at home." Last year's finalists Czech Republic and 2005 winners Croatia also went through to the quarters on Saturday.
Czechs Tomas Berdych and Radek Stepanek followed up Friday's singles successes with a straight-sets doubles victory over Belgium's Steve Darcis and Olivier Rochus in Bree.
In Varazdin, Croatian pair Marin Cilic and Ivo Karlovic, who won their singles on Friday, teamed up to see off Ecuadorian brothers Nicolas and Giovanni Lapentti.
"It wasn't one-way traffic in the doubles, it was as tough as we expected it to be, and we are overjoyed to have secured a berth in the last eight," Cilic said in a courtside interview.
The Czechs will next play Chile or Israel, whose tie was rescheduled to start on Saturday because of the disruption caused by last weekend's earthquake.
Nicolas Massu battled back from a set down to beat Dudi Sela in four sets in the opening singles in Coquimbo with Fernando Gonzalo due to play Harel Levy later.
Croatia will face the United States or neighbors Serbia.
Bob Bryan and John Isner gave the US a lifeline in Belgrade on Saturday by winning a tight doubles rubber against Janko Tipsarevic and Nenad Zimonjic following Friday's singles victories for world No. 2 Novak Djokovic and Viktor Troicki against Sam Querrey and Isner.
"A quarterfinal clash at home with Serbia looks on the cards and if we meet them it will be a delicately balanced tie," Croatia captain Goran Prpic said.
Doubles specialists Mahesh Bhupathi and Leander Paes kept alive India's hopes by crushing Russian pair Teimuraz Gabashvili and Igor Kunitsyn 6-3, 6-2, 6-2 in Moscow.
India trails 2-1 going into Sunday's reverse singles.
In Stockholm, Argentina drafted in David Nalbandian to partner Horacio Zeballos in the doubles against Robin Soderling and Robert Lindstedt and a straight sets success for the Argentine pair opened a 2-1 lead for the 2008 finalists.
