NAPLES, Italy—Britain held off a comeback attempt from Italy to win the doubles match and take a 2-1 lead in their Davis Cup quarterfinal on Saturday.
Earlier, Murray completed a 6-4, 7-5, 6-3 victory over Andreas Seppi in their delayed singles match.
Britain looked on course for a straight-set victory in the doubles but the Italian duo saved four break points at the start of the third set and went on to get a foothold in the match.
The countries' top players face each other in Sunday's first reverse singles match with Murray looking to seal the victory for Britain against Fognini.
"We managed to convert some chances in the fourth set, Colin came up with some good returns in the end and I felt like we deserved to win," Murray said. "Bolelli played an excellent match, he made it really tough for us and was hitting the ball huge from the back of the court.
"It should be a tough match (against Fognini). Fabio has played very well this year so it'll be a great challenge. But I hope I can have a good match and get us to the semis."
Italy has not lost at home to Britain since 1926 and is hoping to reach the semifinals for the first time in 16 years.
Murray gave Britain the first break of the match with a backhand volley winner past Bolelli. Both Italians then argued with the referee in the final game of the first set following what appeared to be a double-hit from Fleming on a point won by the British team.
That appeared to affect the Italian mindset and Britain raced into a two-set lead, sealing it with a cross-court smash from Fleming as the duo held to love.
The match then turned on its head at the start of the third set.
Britain looked set to take another early advantage but Italy saved four break points and then secured its first break of the match.
Italy rescued another three break points as Bolelli served for the set and took the game when Fleming netted a return.
Bolelli helped Italy break again in the third game of the fourth set with a backhand crosscourt winner as the duo fought back from 40-15 down.
There was then a rapid exchange of breaks as Italy looked on course to level the match when serving for the set.
However, Britain broke again before holding to love and then raced into a 40-0 lead in the final game.
Fognini and Bolelli saved two match points as Fleming first hit into the net, before Murray sent a backhand wide. But Britain secured the match when Bolelli failed to get a return over the net.
Murray's singles match had been suspended Friday night due to fading light, with the British No. 1 leading 6-4, 5-5.
When play resumed, Murray immediately broke and then held his serve to take a commanding lead.
Seppi earned an early break in the third set, but the Italian immediately relinquished his advantage with a double fault to allow Murray to break back.
The two-time Grand Slam champion won five games in a row to seal the match.
Seppi missed four set points in the second set, and then double-faulted to hand Murray the decisive break.