Scrum-half Alessandro Troncon believes Italy's first-ever Six Nations away win signals a new era for Italian rugby.
Troncon was named man-of-the-match
Italy secured only their fourth win in the tournament in their 38th match.
"This is the result of a lot of work," Troncon told BBC Sport."We have played well and I think today is the start of a new era for us.
"For me it is a great day. Two weeks ago I was man-of the-match (against England) but today I have won with my team. I am happy for Italian rugby."
Italy coach Pierre Berbizier, who never won at Murrayfiled as a player, said: "It is a big day for us. It was a great victory for us.
"To win here at Murrayfield is a big memory for Italian rugby.
"You work and work and sometimes you get a result. For us it is very important because it means we can face the future with serenity."