A Novak Djokovic-led Serbia surprisingly fell behind 2-1 at home to Kazakhstan in the Davis Cup first round after he lost in doubles on Saturday.
Meanwhile, Italy and France were first through to the quarterfinals after beating weakened visitors Switzerland and Canada respectively.
Djokovic and Nenad Zimonjic fell to Andrey Golubev and Aleksandr Nedovyesov 6-3, 7-6 (3), 7-5 before a full house in Belgrade. It was the second notable cup win for Golubev and Nedovyesov, who beat Roger Federer and Stan Wawrinka in doubles in 2014.
For Serbia not to lose a third time at home in four ties, Djokovic must beat Mikhail Kukushkin in the first reverse singles on Sunday, then hope 23rd-ranked Viktor Troicki, who lost to Kukushkin on Friday, beats 200th-ranked Nedovyesov in the last rubber.
Djokovic won his only previous match against Kukushkin in three sets in Shanghai in 2014.
Andy Murray won his second point for Britain when he and brother Jamie won in straight sets to lead Japan 2-1, giving Murray a chance to clinch the tie on Sunday against Kei Nishikori. Murray leads their head-to-heads 5-1, but Nishikori won their only indoor match.
Also, the Czech Republic led Germany 2-1 in Hannover, Croatia led 2015 finalist Belgium 2-1 in Liege, Argentina led Poland 2-1 in Gdansk, and the United States led Australia 2-1 in Melbourne.
Italy took nearly eight hours to win the opening singles on Friday in Pesaro, so captain Corrado Barazzutti decided to give his best pair a chance to clinch the tie instead of giving a debut to Marco Cecchinato.
Simone Bolelli and Andreas Seppi, who won the Dubai title last week, beat tired singles players Marco Chiudinelli and Henri Laaksonen 6-3, 6-1, 6-3 in less than two hours on the indoor clay court to help Italy reach its third quarterfinal in four years. With an unbeatable 3-0 lead, they awaited Argentina or Poland.
The Swiss were without Federer and Wawrinka.
France paired unused singles players Jo-Wilfried Tsonga and Richard Gasquet for a third time in the cup to seal victory against Vasek Pospisil and Philip Bester 7-6 (4), 6-1, 7-6 (4) in Guadeloupe.
Canada couldn't make up for the absence of Milos Raonic and Daniel Nestor.
France looks like travelling to the Czech Republic in July.
The Murray brothers finished with an ace to beat Yoshihito Nishioka and Yasutaka Uchiyama of Japan 6-3, 6-2, 6-4 in Birmingham. They didn't face a break point.
''Hopefully, I can play another good one tomorrow and seal the win,'' Andy Murray said of his singles against Nishikori.
Tomas Berdych and Radek Stepanek, who have won two Davis Cups together, defeated Philipp Kohlschreiber and Philipp Petzschner 7-6 (7), 7-5, 6-4 for the Czechs to lead Germany 2-1.
Berdych will be confident of clinching the tie against Kohlschreiber on Sunday, as he has an 8-1 record against Germany's best player.
Croatia was on the brink of dumping out Belgium after Ivan Dodig and Franko Skugor defeated Ruben Bemelmans and David Goffin 7-6 (5), 6-3, 6-1.
Former U.S. Open champion Marin Cilic, who won his singles on Friday, can advance Croatia to the quarterfinals on Sunday with a win over Goffin, who will play for a third straight day.
Poland, making its debut in the World Group, prevented Argentina from winning their tie when Lukasz Kubot and Marcin Matkowski beat Carlos Berlocq and Renzo Olivo 6-3, 6-4, 6-4. Argentina, still leading 2-1 after winning both singles in straight sets, is heavily favored to clinch on Sunday and reach the quarterfinals for the 14th time in 15 years.
On grass in Melbourne, the Bryan twins beat Australia captain Lleyton Hewitt and John Peers 6-3, 6-3, 4-6, 4-6, 6-3 to put the Americans in front in the tie between the Davis Cup's most decorated teams. The reverse singles on Sunday are scheduled to be John Isner vs. Bernard Tomic, and Jack Sock vs. Sam Groth.