Tennis: Devis Cup Group Quarterfinals Results
In the second singles rubber, rescheduled from Friday due to heavy rain, Dusan Lajovic defeated James Ward 6-1, 6-3, 6-2 to pull the hosts level.
Lajovic, the world number 81, easily brushed aside Ward in just one hour and 52 minutes after breaking his opponent's serve in the opening game of the match
But in Saturday's doubles Jamie Murray and Dominic Inglot defeated Filip Krajinovic and Nenad Zimonjic 6-1, 6-7 (2/7), 6-3, 6-4 to move Britain to within one win of the last four.
Krajinovic replaced Janko Tipsarevic, who was easily defeated by Kyle Edmund 6-3, 6-4, 6-0 in the first singles match on Friday.
Serbia, the 2010 champions, are without world number one Novak Djokovic, who pulled out of the quarter-final after his shock third-round exit at Wimbledon and with one eye on the Rio Olympics.
Briton Andy Murray also opted out after claiming his second Wimbledon title by beating Canadian Milos Raonic in the final last weekend.
Ward can win the tie in the first rubber on Sunday against Tipsarevic, but if the Serbian veteran wins then it will come down to a deciding match between Edmund and Lajovic, the two teams' highest-ranked players.
The winners will face either Argentina or Italy in the semi-finals.
Argentina is currently 2-1 in front in their last-eight tie in Pesaro.