The Polish striker not only marked his Champions League debut for Barcelona with three goals, but also became the competition's third highest goalscorer by taking over Real Madrid's Karim Benzema.
The result also marked a maiden Champions League win as manager for Xavi Hernandez.
Franck Kessie opened the scoring for the hosts in the 13th minute before Lewandowski doubled that advantage on the half-hour mark.
Jan Sykora pulled a goal back for the visitors, though that effort proved inconsequential as Lewandowski scored again before half-time.
The Pole completed his hat-trick in the 67th minute before Ferran Torres rounded off the night with a goal of his own just moments later.
Speaking after the game, Barca boss Xavi was lost for words when asked to comment on his star striker's performance.
"Lewandowski is insatiable," he said: "I have ran out of words to praise Lewandowski.
"Hat-trick for Lewandowski today. But not only that, he plays and he makes the team play. He knows the third man, and reads space to perfection. I'm in love. His signing was fantastic."
Xavi added: "We never had any doubts with the signing of Lewandowski. We knew his abilities, his humility, and he had a great desire to sign for Barcelona. He's a marvelous person and professional, really."
The Polish international later added: "I feel great. This competition is close to my heart.
"I'm very proud of our teammates. We controlled the match and this is a very important win for us.
"We know that we have to play well in the first half of the season, stay focused, and score more goals. We have to win every match."