The Wimbledon champion returned early on Saturday to the clay court overlooking the Gulf of Naples to complete a straight-sets victory over Andreas Seppi to level the tie, then teamed up with fellow Scot Colin Fleming to beat Fabio Fognini and Simone Bolelli in an entertaining clash.
Murray and Fleming were cruising after winning the opening two sets 6-3 6-2 but the Italian duo found some form to take the third 6-3 and looked like taking it to a decider before the British pair rallied to win the fourth set 7-5.
It means Murray has the chance to send Britain into the semis for the first time since 1981 if he beats Fognini on Sunday in the first of the two reverse singles.
Switzerland or Kazakhstan await in the last four.
World number 13 Fognini, who beat James Ward on a rain-hit Friday to give Italy, the lead is a formidable opponent on clay, having won all three of his ATP singles titles on the surface in the space of the last nine months.
"It should be a tough match, Fabio's played very well this year, especially on the clay so it'll be a big challenge for me but I hope I can play a good match and win the tie," Murray told Italian TV channel Super Tennis.
Murray has not been in the best of form since returning from back surgery but the world number eight proved too resilient for Seppi in a match that had been suspended due to bad light on Friday with the Wimbledon champion already leading by a set.
After surviving four set points on Friday evening, Murray returned to court leading 6-4 5-5 and proved rock solid to complete a 6-4 7-5 6-3 victory.
The doubles rubber always looked like being a significant factor in the outcome of the tie, adding to the tension as Italy fought back from a dreadful start and then forged 5-3 ahead in the fourth set with some inspired tennis which ignited the fans.
Britain edged it though, to put themselves in pole position.
"We'll find out at the end of the tie if this is a crucial point but it's given us great momentum going into Sunday 2-1 up, it's exactly what we wanted when we woke up this morning so we couldn't be happier right now," said Fleming.
Italy will have to win both singles matches on Sunday if they are to reach the semi-finals for the first time since 1998.
- Sports & Recreation
- Colin Fleming
- Andreas Seppi
- Fabio Fognini
- Simone Bolelli