Murray earned the win that ensured Britain would return to the World Group for the first time since 2008, defeating Ivan Dodig in straight sets 6-4, 6-2, 6-4.
That saw Britain take an unassailable 3-1 lead in the World Group play-off clash with Croatia, a day after Murray and Colin Fleming had put Britain back in front.
They defeated Mate Pavic and Dodig in their doubles tie for a 2-1 lead following Murray's win over 16-year-old Berna Coric and Dan Evans' defeat to the former on day one.
Murray was playing his first Davis Cup tie for two years against the Croatians in Umag but hinted that he will be a regular for Britain in the World Group.
"I am looking forward to the World Group, we get to play some of the biggest countries in world hopefully, the top teams and players," said Murray.
"It is exciting and hopefully I will be part of that next year. I thought it was a pretty good match on my side, I gave him very few opportunities on my serve.
"The crowd got into it right at the end with a couple of match points and coming out to serve for it was tough but I was really happy with the way I played.
"It is different, the atmosphere was pretty hostile, you don't get that in Grand Slam matches but that is something that is special about the Davis Cup, it is a character builder."
And, while Wimbledon champion Murray admitted having played in seven Grand Slam finals helped with his pre-match nerves, he revealed his own pressure to deliver the win.
"I was nervous, I wanted to finish the tie, it was a big match, wanting to get back into the World Group, I didn't want to let the team down," he said.
"I dealt with enough pressure around Wimbledon time and those sorts of matches to know how to get through it and how to conquer the nerves and fears you have before you go on the court."
© Sportsbeat 2013