Pierre-Emerick Aubameyang and Frenkie de Jong completed the scoring in the second half as Xavi Hernandez's side rounded off an unbeaten preseason with their fourth win in six matches.
Barca's LaLiga campaign kicks off next Saturday at home to Rayo Vallecano (watch live on ABC, ESPN+ at 3 p.m. ET), while Pumas return to Liga MX action against Club America next weekend.
Despite a trophyless season last time out, there is excitement at Barca once again following a summer of spending, with Lewandowski, Raphinha, Jules Kounde, Franck Kessie and Andreas Christesen all arriving.
They were all presented to a crowd of over 80,000 before the game, with Lewandowski drawing the loudest roar from supporters following his €45 million transfer from Bayern Munich.
The Poland striker had failed to score in three friendlies for his new club so far, but he took less than two minutes to find the net against Pumas, rounding goalkeeper Julio Jose Gonzalez and finishing from a tight angle after a fine pass from Pedri.