A Valerio Bernabo try and two penalties from Edoardo Padovani had put the Italians ahead but Scarlets took control in the second half.
A stunning kicking display from Steven Shingler - who kicked 23 of his side's 28 points - and a try from Steffan Hughes made sure the Welsh side picked up the win.
And Pivac admitted his side were below par in the first period but was pleased with their reaction after the break.
"It was pleasing because we had a patched-up side," he said.
"The conditions were tricky out there. There were a few errors in the first half that put them into the game.
"Half-time was the key point. We controlled the game from there, kicked a few goals and got in front. We came away with the win which is vital.
"We were disappointed to be behind at half-time, but I thought the boys played very well in the second 40.
"We only had about 33 percent territory in the first half so when we did get the ball in their half we tried to play too much rugby.
"At half-time we talked about getting into the field position and putting pressure on them and that is how it panned out. We controlled it a lot better."
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