World number eight Murray had won the first set on Friday but had to save four set points on his way to levelling the second set at 5-5 before poor light stopped play. (Agencies)
The Briton, who on Thursday had suffered a stomach bug, resumed in positive fashion at the Tennis Club Napoli breaking Seppi at 5-5 when the Italian netted a weak return and holding serve to win the second set 7-5.
Seppi gave Britain's sizeable travelling support a brief scare when he broke Murray in the fourth game of the third set after the Scot double faulted at 15-30 then sent a return into the tramlines to give the Italian a 3-1 lead.
It seemed only to stiffen Murray's resolve, although the Scot met plenty of resistance on his way to breaking back in the next game after Seppi double faulted at serve.
Seppi was less resolute as Murray served out to level and then allowed his opponent to break again in the next game to pull 4-3 ahead.
From then on, Murray had little trouble and as Seppi's confidence began to drain the Scot went on to seal the set 6-3 with relative ease.
Murray said the difference from Friday was his improved service game: "I just think my ability to win more free points on my serve helped."
Davis Cup organisers announced that Murray would replace Ross Hutchins and join Colin Fleming in Britain's doubles, with Fabio Fognini replacing Paolo Lorenzi and teaming up with Simone Bolelli for the hosts.
Murray had said earlier: "I would like to play doubles, you want to help the team as much as possible, but I have to go and speak to the team right now."
On Friday Italy had taken a 1-0 lead in the World Group tie when national number one Fognini beat James Ward, ranked 161 in the world, 6-4, 2-6, 6-4, 6-1.
Italy last advanced to the World Group semi-finals in 1998 when they went on to finish runners-up to Sweden, while the last final-four appearance for Britain -- nine-time winners but who last triumphed in 1936 -- came in 1981.
The eventual winners will take on either Switzerland or Kazakhstan in September's semi-finals.
World number eight Murray had won the first set on Friday but had to save four set points on his way to levelling the second set at 5-5 before poor light stopped play.