The Poland striker opened his account on the half hour and doubled it four minutes after the re-start to give embattled Bayern a much-needed boost, a day after club bosses launched a scathing attack on the media while backing coach Niko Kovac and his players despite their dip in form.
"We had a lot of pressure," Kovac told reporters. "We wanted everyone to focus over 90 minutes and give it all for the club. The team did this unusually well and the final score is fully deserved.
"Overall it was a solid performance, even when we were down to 10 men. Even when they pulled a goal back we did not falter."
The game looked to be turning for the hosts in the 57th minute when Bayern winger Arjen Robben was sent off after a second booking. It was the Dutchman's first dismissal in more than seven years.
The Wolves then cut the deficit through Wout Weghorst six minutes later and launched an all-out offensive in search of the equaliser before James Rodriguez stunned the home crowed with a curling shot following a Lewandowski pass.
The win will no doubt ease some of the pressure on Kovac, in his first season at Bayern, and the team can earn more bonus points with fans if they beat AEK Athens in Greece in the Champions League next week.
Bayern, whose president Uli Hoeness and CEO Karl-Heinz Rummenigge on Friday accused the media of unfair and "shameful" reporting of their team's current form, are now in third place on 16 points, four behind leaders Borussia Dortmund, and one behind second-placed Werder Bremen, who beat Schalke 04 2-0.
(Reporting by Karolos Grohmann; Editing by Tony Lawrence and Pritha Sarkar)
