World number one Novak Djokovic powered Serbia into the Davis Cup quarter-finals on Saturday while France also advanced.
Djokovic's Serbia took an unbeatable 3-0 lead over Croatia, while France ensured a victory over Germany in World Group first-round play.
But defending champions Switzerland, missing big guns Roger Federer and Stan Wawrinka, face being dumped out of the team tournament in the first round as Belgium took a 2-1 advantage by winning the doubles in Liege.
The United States kept their hopes alive against Great Britain in Glasgow despite Mike and Bob Bryan, the top doubles team in the world, being pegged back to two sets all after winning the opening two frames against Jamie Murray, the brother of Davis Cup teammate Andy Murray, and Dom Inglot.
The twins kept the Americans in the contest ahead of Sunday's singles with a 6-3, 6-2, 3-6, 6-7 (8/10), 9-7 victory.
Andy Murray, the world number five, and James Ward, ranked 111, had gotten Britain off to a 2-0 start on Friday.
Former Wimbledon and US Open champion Murray can clinch a quarter-final meeting with France if he defeats John Isner in Sunday's first reverse singles. A defeat for the Scot would leave Ward and Donald Young to clash in the deciding rubber.
- Djokovic doubles duty -
There were early celebrations in Kralijevo after Djokovic came in as a last-minute doubles replacement for Viktor Troicki and alongside Nenad Zimonjic convincingly beat Marin Draganja and Franko Skugor 6-3, 6-4, 6-1.
The Serbian pair needed less than two hours to advance, despite a scare in the second set when Djokovic was treated for a blister on his right hand.
"We wanted to finish the job today, to take advantage of the fact that we won the first singles and that was done," said the 27-year-old Djokovic.
Djokovic had easily beaten Mate Delic on Friday as the 2010 winners grabbed a 2-0 lead over a Croatia team missing injured US Open champion Marin Cilic.
Serbian captain Bogdan Obradovic decided to rest Troicki after his three-hour victory over teenage sensation Borna Coric, when he fought back from two sets down.
The Serbian pair held serve in the opening set before Davis Cup debutant Skugor cracked following a powerful Djokovic backhand down the middle and the hosts took the opening set 6-3 before sailing through in the final two frames 6-4, 6-1.
Serbia will next face either Brazil or Argentina.
Brazil seized a 2-1 lead in Buenos Aires after Marcelo Melo and Bruno Soares defeated Diego Sebastian Schwartzman and Carlos Berlocq 7-5, 6-3, 6-4 in doubles.
In Frankfurt, France assured themselves of a quarter-final berth when Julien Benneteau and Nicolas Mahut posted a 6-4, 6-3, 6-2 doubles success over Benjamin Becker and Andre Begemann.
Gilles Simon and Gael Monfils had put France 2-0 up after beating Jan-Lennard Struff and Philipp Kohlschreiber respectively on Friday.
"It's been the perfect weekend in terms of results and for the doubles pairing," said France captain Arnaud Clement, whose side lost the 2014 final on home soil against Switzerland.
"We have seen in the past how difficult it can be for teams to play well again having reached the final the year before, so it was important to see the enthusiasm in this first match."
Germany have now lost all eight Davis Cup matches against the French dating back to 1938.
In Ostrava, the Czech Republic kept their hopes alive 2-1 with Jiri Vesely and Adam Pavlasek beating Australia's Lleyton Hewitt and Samuel Groth 1-6, 7-6 (7/2), 3-6, 7-6 (7/4), 6-2 in the doubles.
The Australians had been 2-0 up overnight after teenager Thanasi Kokkinakis stunned top Czech Lukas Rosol 4-6, 2-6, 7-5, 7-5, 6-3, with Bernard Tomic then seeing off Jiri Vesely 6-4, 6-3, 7-6 (7/5).
The winner will meet either Italy or Kazakhstan.
- Fognini/Bolelli shine again -
Fabio Fognini and Simone Bolelli gave the Italians a 2-1 lead in Almaty, the Australian Open champions beating Andrey Golubev and Aleksandr Nedovyesov 7-6 (7/4), 6-3, 6-7 (13/15), 6-4 in a match which lasted three hours and 18 minutes.
In Liege, Belgian doubles pairing Ruben Bemelmans and Niels Desein saw off Adrien Bossel and Michael Lammer 1-6, 6-3, 6-2, 6-2 to put the hosts on course for their first quarter-final in eight years.
Bemelmans lost his opening singles rubber to Switzerland's Henri Laaksonen, with Steve Darcis pulling the hosts level.
The winner will face either Canada or Japan.
Canada were in control in Vancouver after Daniel Nestor and Vasek Pospisil outlasted Japan's Go Soeda and Yasutaka Uchiyama 7-5, 2-6, 6-3, 3-6, 6-3 to put the hosts up 2-1.
That means 2014 US Open runner-up Kei Nishikori, ranked fourth in the world, will be fighting to keep Japan alive when he takes on world number six Milos Raonic in Sunday's first reverse singles match. Both Raonic and Nishikori won singles matches on Friday.