The German and European champions' 32-game unbeaten streak was ended in a shock 4-1 loss at Hoffenheim last weekend and they nearly dropped two more points on Sunday.
Lewandowski had put Bayern two goals in front - the second assisted by full debutant Chris Richards - but Jhon Cordoba powered in a header with almost an hour played and Matheus Cunha scored an impressive equaliser soon after.
The prolific striker's hat-trick goal was then instantly cancelled out by Jessic Ngankam in an incredible second half, but Lewandowski won a penalty in stoppage time that he stepped up to convert as Bayern got back to winning ways in the league.
Hertha thought they had the lead inside 15 minutes, only for Cordoba's thumping strike to be ruled out for offside.
Bayern had an offside goal of their own chalked off by VAR when Thomas Muller headed in from close range, though they were in front four minutes later via Lewandowski.
Alexander Schwolow parried Lewandowski's initial header but the ball was sent back to the edge of the six-yard box and the striker volleyed in.
Lewandowski's landmark 100th Bundesliga goal at the Allianz Arena arrived five minutes into the second half as he collected Richards' pass inside the box, worked a bit of space and arrowed a shot into the bottom-left corner.
But Cordoba headed in Cunha's free-kick to pull one back, before the latter exchanged passes with substitute Krzysztof Piatek to coolly tuck past Manuel Neuer and equalise.
Bayern, who beat Borussia Dortmund 3-2 to win the DFL-Supercup in midweek, temporarily restored their lead thanks to Lewandowski's tap-in after Muller helped on a free-kick with 85 minutes on the clock.
The visitors levelled once again two minutes from time - Ngankam, on the field for 64 seconds, stooping in to head past Neuer.
But there was still time for one last twist as Lewandowski was dragged down in the box and stepped up to win the match for Hansi Flick's men.
Lewandowski the four-goal hero
Perhaps the biggest factor in Bayern's loss to Hoffenheim last week was that Lewandowski did not start - the first time in two years he had been benched for a league game.
In the week he was named UEFA Men's Player of the Year for 2019-20, he showed yet again why he is the best striker in the world with four more goals here from 13 attempts.
