Marc-Andre ter Stegen kept a fifth consecutive clean sheet in the top flight and, along with Lewandowski's brilliantly taken strike in the 20th minute, it was enough to put Barcelona one point clear of Real Madrid, who host Osasuna on Sunday.
In Mallorca, Xavi Hernandez's side demonstrated they are ironing out the creases which caused them so many problems last season, improving both defensively and in attack, with the relentless Lewandowski leading the charge.
Barcelona's coach earned a new domestic record of 18 consecutive league matches on the road without defeat, moving ahead of former Real Madrid coach Zinedine Zidane.
Ter Stegen, who has started this season in top form, beat his own personal record of 500 minutes without conceding in La Liga, reaching 534 minutes and counting.
At the other end, Lewandowski leads the scoring charts in Spain on nine goals from seven games, after clinically curling into the bottom corner to break the deadlock against Mallorca.
Xavi deployed young left-back Alejandro Balde out of position on the right side of his defence because of injuries to Ronald Araujo, Jules Kounde and Hector Bellerin, and brought Ansu Fati into the starting line-up.
It was the 19-year-old's first start in La Liga since November 2021, after a string of injury problems, and his burst forward contributed to Barcelona's opening goal.
The winger, left out of Luis Enrique's most recent Spain squad and desperate to impress to try and get the call-up for the World Cup, fed Lewandowski, who cut inside and finished like few others can.
Mallorca should have levelled 15 minutes later but Marc-Andre ter Stegen made a superb save to deny Jaume Costa from close range.
Barcelona struggled to create more openings and the game threatened to boil over, with a flurry of bookings and Xavi's assistant and brother, Oscar Hernandez, being issued a red card for apparent dissent.
Kang-in Lee sent a shot agonisingly wide of the far post as Mallorca tried to hit Barcelona on the counter at the death.
In previous seasons Barcelona might have caved, but Xavi's side are starting to prove their fortitude.
"Generally we did very well, we limited them to just two chances, Ter Stegen made a brilliant save and Lewandowski scored a great goal," said Xavi.
"(However) it would be poor to limit it to that. We defended very well. They are players that make the difference, but I would say the team competed well."