Having won by a point last time out against Edinburgh, the Scarlets were particularly disciplined in defence, as they withstood a barrage of Ulster attacks late on, and Kiwi coach Pivac was quick to congratulate his team.
Pivac said: "It was a tremendous team effort this afternoon. This game, along with our performance against Leinster away, has been our best all season and we're delighted that the result has gone our way.
"We didn't play well the last time we were out here in Ireland with a disappointing performance, and result, against Connacht.
"Not many teams come here and win so it's really pleasing to have been able to do so today - the first time since 2008 I believe.
"We've been dealing with discipline internally and have kept all 15 players on the pitch for the second week in a row.
"Our penalty count was under 10 and we're really proud of them working hard for each other.
"The weather has been challenging when you're trying to play a more expansive game and spread a little more of the ball. What was pleasing was that we were able to do more of that but also of what we were able to do in defence.
"We got ourselves in the game early which had been our goal all week and a big defensive effort in the second half kept us ahead and got the all-important victory and four points."
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