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Lewandowski and Ousmane Dembele both went close for Barca, hitting the post in the first half, but it did not take long for them to open the scoring, as Lewandowski stroked home from close range from a perfect Raphinha cross to the far post in the 24th minute.
Barcelona extended their lead right before half-time through Pedri, who riffled a curling strike into the top-left corner after a nice pass by Dembele from the right touchline.
Lewandowski scored Barca's third in the 65th minute, with a brilliant back-heel that deflected off a defender before beating goalkeeper Jordi Masip.
The Poland striker had a golden opportunity to complete a hat trick in added time, but Masip made a great stop to keep out his close range shot.
Substitute Sergi Roberto, however, was in the right place at the right time to strike home the rebound and wrap up the points.