Yuki, who had lost the first set 3-6 against the Serb, was 4-4 into the second when rain played spoilsport in the World Playoff tie.
Yuki, 22, had lost against Dusan Lajovic 3-6 2-6 5-7 in the opening tie, but is fighting hard in the reverse singles match.
Earlier, a resilient Somdev won the battle of nerves and wits as he pulled off a stunning five-set victory over World.61 Dusan to lock the Davis Cup World Group play-off tie against Serbia 2-2.