Following Alejandro Balde’s low cross, the ex-Bayern Munich striker scored his first goal in 47 seconds.
Six minutes later, Alexander Isak equalized with a shot that looped in.
Lewandowski sidefooted in a third goal, Ousmane Dembele’s low shot made it 2-1, and Ansu Fati quietly tacked on a fourth.
The impressive result was appreciated after Barca’s lackluster season opener, a 0-0 draw against Rayo Vallecano at home.
Lewandowski left Bayern with only one year remaining on his contract and joined Barca in the summer for £42 million. Rafinha, a Brazilian attacker who once played for Leeds United, entered the game as a substitute in the second half.
However, Jules Kounde, a central defender for France, was ineligible to play for Barcelona since he is yet to register as a player after moving from Sevilla at the end of July for financial reasons.
In addition to playing Manchester City on Wednesday in a friendly, Barca, now sixth in La Liga, will face Valladolid at the Nou Camp on Sunday.