Williams was playing for the first time since last September and scored in the 11th minute and had a hand another try.
The Wales international was substituted after 52 minutes to save him for next week's Pro12 showdown with Munster.
"I didn't expect him to go that well to be honest with you. If anything I thought he over-achieved," said Pivac.
"I thought he played very very well first game back.
"His decision making, the timing of the pass just to hold the defenders and put guys away - that's class.
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"I guess it would have put a smile on [Wales coach] Warren Gatland's face with the summer tour just around the corner."
Wales play a three-test series against New Zealand in June.
Williams suffered knee ligament damage in Wales' 2015 World Cup pool win over England at Twickenham.
The match against Dragons was the centre's first of the season for Scarlets, who could yet claim a place in the Pro12 play-offs.
If they beat Munster in Thomond Park next week and Ulster lose at Ospreys, Scarlets will clinch fourth place.
Williams said he wanted to get "a good week training" before the match in Munster after a pleasing return.
"It was better than I thought," he said.
"It's great to be back - it's been a long time and I'm just happy to be back with the boys.
"But it was tiring and I thought I might not make it to half time."
Asked about his Wales tour prospects, Williams said he was just concerned with the Scarlets' remaining match.
"Those things are out of my hands," he added.
Coach Wayne Pivac praised Scarlets centre Scott Williams after his try-scoring return in the 34-20 Pro 12 win over Dragons on Judgement Day IV.