Davis Cup holders Britain edged into a 2-1 lead in Serbia after Jamie Murray and Dominic Inglot won Saturday's doubles.
Rain meant only one of Friday's two scheduled singles were completed but Serbia quickly squared up the quarter-final on day two as Dusan Lajovic thrashed James Ward 6-1, 6-3, 6-2.
However, Murray and Inglot were too strong for veteran Nenad Zimonjic and Filip Krajinovic, winning 6-1, 6-7(2), 6-3, 6-4 to put Britain one rubber away from the semi-finals.
Serbia are without world number one Novak Djokovic while Wimbledon champion Andy Murray travelled with his British team mates but will not feature in the tie.
In other action Argentina lead Italy 2-1 in Pesaro while Wimbledon doubles champions Nicolas Mahut and Pierre-Hugues Herbert won Saturday's doubles to give France a 2-1 lead over the Czech Republic.
The U.S. lead Croatia 2-0 in the other World Group tie.
Croatia still alive in quarter-final
Croatia kept alive their Davis Cup hopes when Marin Cilic and Ivan Dodig won their doubles match in four sets against the United States in Oregon.
Cilic was not expected to play doubles, but was drafted in at the last minute after Croatia lost both singles rubbers on Friday to slip to the brink of elimination.
And the 2014 U.S. Open singles champion teamed up superbly with Dodig against American doubles specialists the Bryan brothers, Bob and Mike, winning 6-2, 2-6, 6-2, 6-4 in Portland.
"I played probably the best match in my life in doubles, especially at this kind of occasion," Cilic told Tennis Channel.
The U.S. lead 2-1 heading into Sunday's reverse singles, while Davis Cup holders Britain also enjoy a 2-1 lead in Serbia after Jamie Murray and Dominic Inglot won Saturday's doubles.
Rain meant only one of Friday's two scheduled singles were completed but Serbia quickly squared up the quarter-final on day two as Dusan Lajovic thrashed James Ward 6-1, 6-3, 6-2.
However, Murray and Inglot were too strong for veteran Nenad Zimonjic and Filip Krajinovic, winning 6-1, 6-7(2), 6-3, 6-4 to put Britain one rubber away from the semi-finals.
Serbia are without world number one Novak Djokovic while Wimbledon champion Andy Murray travelled with his British team mates but will not feature in the tie.
In other action Argentina lead Italy 2-1 in Pesaro while Wimbledon doubles champions Nicolas Mahut and Pierre-Hugues Herbert won Saturday's doubles to give France a 2-1 lead over the Czech Republic.
