The Poland international, 33, joined the Catalans this summer for a fee of €45 million from Bayern Munich and has wasted little time making his mark.
Wednesday's treble took Lewandowski to eight goals in just five games for Barca, but Xavi was quick to point out the player brings more to the team than just goals.
"That's how Robert is, insatiable," Xavi said. "The way he trains, the way he helps the team, his humility, his work-rate ... I can't praise him enough because it's not just about his hat-trick, it's the way he works, how he knows to dominate the tempo of the game."
Franck Kessie put Barca in front in the 13th minute, heading in his first goal for the club following a corner.
Lewandowski extended their lead with a right-footed finish into the bottom corner in the 37th, after Barca had survived a scare which almost led to them conceding a penalty and having a man sent off.
Viktoria were awarded a penalty and Barca defender Andreas Christensen was shown a red card for hauling down Jhon Mosquera but a VAR review showed Mosquera had struck Christensen with an elbow and the decision was overturned, the Plzen forward being shown a yellow card instead.
Plzen pulled themselves back into the game in the 44th minute with a header from Jan Sykora but Barca quickly restored their two-goal cushion when Lewandowski produced a diving header from an Ousmane Dembele cross in first-half stoppage time.
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The Poland striker completed his treble midway through the second period, meeting a layoff from Ferran Torres and curling the ball inside the far post with one touch.
“I knew from the beginning here it was going to be important to adapt right from the first game," Lewandowski said. “People ask about the goals, but it’s important to be in the right position, to help my team because my teammates have helped me a lot on and off the pitch.”
Lewandowski said the goals were a gift to his wife, who was at the Camp Nou celebrating her birthday.
“The fact that she was in the stadium on her birthday means a lot," he said. "Something amazing for me.”
It was Lewandowski's sixth hat-trick in the Champions League and he became the first player in the competition's history to score one for three different clubs, having netted trebles for Bayern and Borussia Dortmund.
Torres completed a hugely satisfying evening for Xavi 's side by scoring the fifth goal to put Barca top of Group C. They head to Bayern next on September 13, when Plzen host Inter Milan.