The Wimbledon champion beat Ivan Dodig, ranked 35th in the world, 6-4, 6-2, 6-4 to claim the best-of-five World Group play-off on the Umag clay courts, reports Xinhua.
Murray met no challenge from the Dodig and showed no signs of a recent back injury.
The 26-year-old Murray, who played his first Davis Cup tie in two years, won both his singles matches and paired with Colin Fleming to win Saturday's doubles rubber.
Britain will next take on another of the world's top 16 nations in the first round of the World Group in February.
--IANS (Posted on 16-09-2013)