Tommy Robredo and Marcel Granollers came through for defending champion Spain to lead the gritty Swiss 2-1, and David Nalbandian helped swing the tie in Stockholm in Argentina's favor.
Meanwhile, Nicolas Massu and Fernando Gonzalez each won their singles in four sets against Israel to give Chile's first-round tie a much-needed positive start following the deadly earthquake and tsunami.
France failed last year to reach the quarterfinals for the first time since 2000, but secured an unbeatable 3-0 lead against Germany when Michael Llodra and Julien Benneteau defeated Philipp Kohlschreiber and Christopher Kas 6-1, 6-4, 1-6, 7-5 in Toulon.
Benneteau and Llodra won the Marseille title last month but were paired in Davis Cup for the first time. Benneteau, on debut, nailed their second match point with a forehand volley winner.
"The 3-0 score is the ideal and the manner was there, too," France captain Guy Forget said.
In Varazdin, Friday singles winners Marin Cilic and Ivo Karlovic teamed up to beat brothers Nicolas and Giovanni Lapentti 7-6 (3), 6-3, 7-5 for the vital third point.
"Even I didn't expect it to be that easy," Croatia coach Goran Prpic said. "This gives us a confidence to believe that we can move further than last year," when Croatia was ousted in the semifinals by the Czech Republic.
The Czechs advanced thanks to Tomas Berdych and Radek Stepanek, who also won Friday's singles, beating Olivier Rochus and Steve Darcis of Belgium 7-6 (0), 6-0, 6-3 in Bree.
Berdych and Stepanek, who led the Czechs to their first final in 29 years last year, didn't drop a set against the Belgians.
"I still can't believe how great the guys played this weekend," Czech captain Jaroslav Navratil said. "With a team like this I am confident against any nation."
Defending champion Spain gained control against Switzerland when Robredo and Granollers beat Stanislas Wawrinka and Yves Allegro 7-6 (8), 6-2, 4-6, 6-4 under the roof of the Logrono bullring.
On Sunday, Spain's David Ferrer will play Wawrinka with a chance to seal a 3-1 win and meet France in the quarterfinals.
Mahesh Bhupathi and Leander Paes, one of tennis' greatest teams, stopped Russia from wrapping up the tie in Moscow by steamrolling first-time pair Igor Kunitsyn and Teimuraz Gabashvili 6-3, 6-2, 6-2.
Bhupathi and Paes, winners of 10 Grand Slam doubles titles and unbeaten in 23 consecutive Davis Cup doubles, took only 96 minutes.
Yet Mikhail Youzhny should still secure the win in the first reverse singles on Sunday against Somdev Devvarman, and keep Russia unbeaten at home since 1996.
Another great duo, the top-ranked Bryan twins, didn't play together in Davis Cup for the first time, yet Bob Bryan paired with rookie John Isner to beat world No. 1 doubles player Nenad Zimonjic and Janko Tipsarevic 7-6 (8), 5-7, 7-6 (8), 6-3 to keep the United States alive, and cut Serbia's lead to 2-1 in Belgrade.
Bob Bryan's twin Mike was sidelined with food poisoning.
"It definitely was a new experience for me, we pulled a couple of amazing tiebreakers," Bob said.
Isner will play for a third straight day on Sunday in the first reverse singles against Novak Djokovic, who has a chance to deliver Serbia's first win in the World Group before an adoring home crowd and set up a quarterfinal against Croatia.
The Croatians, the 2005 Davis Cup champion, hope their neighbors do it. The two countries fought a war in 1991, and while they've since vastly improved relations, tensions between the two nations still occasionally flare up.
Prpic said if their opponent is Serbia, "it'll be exciting."
In Stockholm, last-minute arrival Nalbandian was rushed into the doubles and partnered newcomer Horacio Zeballos for the first time to defeat Robin Soderling and Robert Lindstedt 6-2, 7-6 (4), 7-6 (5) and give Argentina a 2-1 lead against Sweden.
Despite playing only his fourth match since hip surgery last May, Nalbandian didn't lose his serve, and got stronger as the match progressed.
"For being the first time we play together I think it's excellent," he said.
Nalbandian could yet to recruited into the reverse singles on Sunday. The winner of the tie will meet Russia.
In Coquimbo, at the tie delayed by the earthquake and tsunami, the home team gave their fans a welcome boost by sweeping both singles from 2009 semifinalist Israel.
Massu and Gonzalez both lost their first sets, then dictated the action. Massu beat Dudi Sela 4-6, 6-2, 6-2, 6-4, rallying from 3-1 down in the fourth. Gonzalez topped Harel Levy 2-6, 6-3, 6-4, 6-4.