Carlo Ancelotti's defending champions were confronted by a stubborn wall of green defence as clear-cut chances dried up during the second half at Weser-Stadion.
It was left to Lewandowski to produce a wonderfully instinctive finish in the 72nd minute, just as Bayern's hopes of starting the campaign with back-to-back wins appeared to be dwindling.
The Poland star added a second three minutes later to make it six for the season across four outings in all competitions.
Lewandowski was a virtual bystander in the first half, when Corentin Tolisso struck the crossbar and Arjen Robben wasted Bayern's best chance.
Ancelotti's side travel to Hoffenheim after the international break, by which time Renato Sanches might have secured a move away from the club.
Bayern pinned their hosts back during the opening stages and almost took a seventh-minute lead –Tolisso volleying against the top of the bar when Werder goalkeeper Jiri Pavlenka failed to claim following a corner.
There was impressive work from Pavlenka when he got down to beat away David Alaba's piledriver before Werder threatened at the other end.
Mats Hummels blocked Thomas Delaney's shot in the 29th minute and was relieved to see centre-back partner Niklas Sule clear Ludwig Augustinsson's attempt from the loose ball off the line.
Bayern launched a fresh assault before the break, with Robben unmarked and glancing wide from Franck Ribery's left-wing cross.
The former France winger then went on a marauding run into the area, only to be denied by Pavlenka.
Werder's massed defensive ranks frustrated Bayern after the restart, with the champions forced to subsist on a diet of speculative, long-range efforts.
With 64 minutes played, Ancelotti turned to Kingsley Coman as a replacement for Robben and the substitute's incisive pace proved a key factor when the deadlock was broken shortly afterwards.
The France international fashioned enough space to thread a low cross from the right channel and Lewandowski stole in front of Lamine Sane at the near post to dispatch a superb backheel finish.
Following that finesse came force, as Lewandowski collected a pass from the recently introduced Thomas Muller and surged towards a backpedalling Werder backline.
He momentarily seemed to lose control of the ball but steadied himself to fire a shot through Pavlenka's legs and seal the points with 15 minutes remaining.
It meant consecutive defeats for Alexander Nouri's Werder, who travel to Hertha Berlin when the Bundesliga resumes.