The Wimbledon champion brought Great Britain level at 1-1 when he swept aside Andreas Seppi 6-4 7-5 6-3 in a match held over from day one.
He then teamed up with Colin Fleming in the doubles to produce a 6-3 6-2 3-6 7-5 victory over Simone Bolelli and Fabio Fognini.
It gave Britain a 2-1 lead going into Sunday's reverse singles, following Jamie Ward's defeat to Fognini in Friday's opening rubber.
Murray started his match against Seppi one set up and level at 5-5 in the second and wasted little time in strengthening his hold on the contest.
He took the opening two games of the day to move 2-0 up in sets before his opponent threatened to stage a comeback as he broke for a 3-1 lead in the third.
Murray, though, hit back, rattling off five straight games to seal victory in three hours and seven minutes.
On Thursday there had been doubt whether he would take to the court at all as he battled a virus, while the condition of the clay court caused problems.
However, Murray then teamed up with Fleming in the doubles.
The decisive break in the first set came in the eighth game after Fognini double faulted, then smashed long, before the Scot took over.
There was a scare in the opening set when Louis Cayer appeared to collapse at the side of the court. However, the incident involving Britain's doubles coach did not appear to be serious.
Britain broke in the third game of the second set following a Bolelli error - then in the seventh when Murray's return down the line was too good for Fognini.
However, Italy broke in the fourth game of the third set and saw it out to reduce the deficit to 2-1.
The fourth set was a see-saw affair, with Britain securing the fifth break of serve - and the match - by taking the third break point available.
Sunday's singles see Fognini take on Murray, while Seppi takes on Ward.