And Pivac claims his side are on a roll ahead of their two remaining matches against Cardiff Blues and Treviso - and praised the presence of not just the impressive Williams but skipper Ken Owens, Jake Ball, Scott Williams and John Barclay.
"Qualification is in our own hands now, we need to build on this performance and not think past the Blues," he said.
"It was obvious that our international boys lifted our standards. This is their backyard and they set an example and led really well, which is very pleasing.
"I think Liam made one error in the entire match. He's a class player and proved it.
"We needed the five points after Edinburgh winning. There are parts I'm not happy with, our discipline let us down at times but the scrum went well."
With two matches remaining, the Scarlets enjoy a slender one-point advantage over seventh-placed Edinburgh and are five ahead of Connacht, who were beaten 31-13 by high-flying Glasgow.
Meanwhile, Dragons director of rugby Lyn Jones blamed his side's lack of experience for their defeat in front of a crowd of over 50,000 in Cardiff.
"It was a poor game from both sides. We made three errors before the break and gave them 20 points or more and that was the difference," Jones said.
"We have not played well in the last eight days but we are still a good side. We just didn't prove that unfortunately.
"We've got some great young players but there's not enough experience around them to help improve their game."
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