Lewandowski’s ninth strike in the league was enough to seal the victory, but Barça also needed goalkeeper Marc-Andre ter Stegen to be in top form.
The win temporarily takes Barça ahead of Real Madrid at the top of the table.
Madrid will look to maintain their 100% winning start to LaLiga on Sunday when they host Osasuna.
With Ronald Araujo, Jules Kounde and Hector Bellerin all injured, Xavi Hernandez picked Alejandro Balde at right-back in Mallorca, while Gerard Pique and Jordi Alba also came into the side.
It was the ever-present Lewandowski who opened the scoring in the 20th minute.
The Polish striker collected an Ansu Fati pass before cutting back inside his man and unleashing a fine finish into the bottom corner through a mesh of bodies.
It was his 12th goal in all competitions this season and served to win the game for Barça.
Xavi’s side had to endure some nervy moments to hold on to the win, with Javier Aguirre’s Mallorca impressed.
Ter Stegen saved from Jaume Costa and Antonio Sanchez, with Lee Kang-In shooting wide late on as Barça picked up three valuable points.