With a try in the opening minutes Glasgow looked on course to kick on and secure a valuable winning bonus, but head coach Danny Wilson was satisfied with the four points.
"We can take four points out of it, that's important," he said in The Scotsman. "I said before the game 'Boys, we're currently a top-four team. Top-four teams come here and do the job'.
"We've come here and to an extent we've done the job. We've got the four points we needed.
"Granted, we wanted five, and we haven't got them because of not a great performance. But if we can play as poorly as in that second half and still hold on and win in Italy, I'll take that. But I think we all know we've got to be better next week facing Leinster at home."
Glasgow look set to have a number of other key players back to face Leinster. British & Irish Lions Ali Price and Zander Fagerson could be involved for the first time this season while Sam Johnson and Kyle Steyn should also return after being rested. Australian international Jack Dempsey should be back after he and Matt Fagerson - who is more of a doubt for Friday - were ruled out of this game at the last minute by illness.
"We've had a lot of disruption this week and we've come away with four points," Wilson continued. "So we've got to take the positive of that first of all.
"Our second-half performance was poor. But like I said, we've come out of here with a win. That's three wins on the bounce, we're still fourth in the league, we'll take that."
A downside of this match was the injury to Fraser Brown that looks likely to rule him out of the Leinster game at Scotstoun on Friday, and may well also necessitate his missing Scotland's autumn internationals too. "It doesn't look great at the moment," Wilson added. "It's a knee injury that will need to be scanned. It's tough for him."