Departing Andy Roddick and James Blake left clean-up operations to the California Bryan brothers a day after the doubles pair iced weekend victory 3-0.
In Sunday's first dead rubber, cramping Mike Bryan retired to hand over a 7-5, 1-0 win to Austria's Stefan Koubek. Bob Bryan concluded over Werner Eschaeur 6-0, 3-6, 7-6 (7-3) as the Austrian saved four match points before going down.
"It's tough to play a Grand Slam with Davis Cup right on the horizon, but these are the only real moments that get my juices flowing anymore," said Bob Bryan.
The US face next France April 11-13 in Winston-Salem, North Carolina, the well-attended venue for a 2007 win over Spain in a region which sees no professional tennis on a regular basis.
"It was one of the best crowds we've ever had in the US," said US captain Patrick McEnroe. "We hope to fill it again and make it nice and loud and noisy for the French."
France piled on two more points on Sunday to finish off Romania 5-0.
Michael Llodra beat Andrei Pavel 7-6 (7-5), 7-6 (9-7) in a dead rubber while Arnaud Clement defeated Horia Tecau 7-6 (7-3), 2-6, 6-4.
In Moscow, illness caught up with Novak Djokovic, as the Serbian world number three could not go on in his key singles rubber against Nikolay Davydenko.
Davydenko clinched a quarter-final place for 2006 champion Russia as he won 4-6, 3-6, 6-4, with Australian Open winner Djokovic felled by the influenza which kept him out of Friday play.
Djokovic, known for a fragile physique, was later taken to hospital for a check-up, team officials said.
"I didn't want to risk my health," said the Serb. "I was feeling very dizzy, I was losing a lot of energy. It's not easy to play when you have a virus infection."
Russia got a 3-2 trip into the last eight and a matchup with the Czech Republic. Viktor Troicki beat Russian Dmitry Tursunov in the final match 7-6 (9-7), 4-6, 6-3.
Veterans Thomas Johansson and Jonas Bjorkman worked their experience to perfection to salvage a 3-2 win for Sweden over Israel.
Johansson began the comeback effort 7-6 (8-6), 6-1, 7-5 over Dudi Sela while Bjorkman rallied from a horror opening set to clinch the final rubber against Harel Levy 0-6, 6-4, 6-3, 7-6 (8-6).
In Braunschweig, Philipp Kohlschreiber advanced Germany into a quarter-final with Spain as he secured the winning point over South Korea's Lee Hyung-Taik 6-0, 4-6, 6-1, 7-6 (7-1) to ensure an untouchable 3-1 lead.
By Bill Scott, dpa