Although Hoffenheim appeared to have weathered the storm and looked comfortable midway through the first half, they were undone by a set piece as Kimmich's corner was headed home by Thomas Muller.
The visitors went on to employ the physical approach during the remainder of the opening 45 minutes and Bayern responded in kind, with five yellow cards and an injury to Kingsley Coman before the break.
For all of Hoffenheim's struggles during the game, they managed to equalise against the run of play when Adam Szalai got the better of Jerome Boateng before firing across Manuel Neuer just before the hour.
The game then endured a chaotic finish as Bayern were awarded a penalty, but Lewandowski's spot kick had to be re-taken due to encroachment from Arjen Robben, who scored the rebound after the Pole's effort was saved.
Lewandowski made no mistake at the second opportunity, but minutes later, the hosts had another goal ruled out after the referee judged Muller to have handled Leon Goretzka's shot before it hit the net.
Nonetheless, Niko Kovac's side succeeded in killing off the game on 90 minutes, Robben rifling home from a tight angle to ensure a winning start for the 2017-18 champions.
BAYERN MUNICH (4-1-4-1): Neuer; Kimmich, Sule, Boateng, Alaba; Martinez (Goretzka 67'); Coman (Robben 45'), Muller, Thiago, Ribery (Rodriguez 83'); Lewandowski
HOFFENHEIM (3-5-2): Baumann; Bicakcic, Vogt (Nordtveit 74'), Nuhu (Akpoguma 67'); Kaderabek, Bittencourt, Grillitsch, Grifo (Zuber 45'), Schulz; Apolinario, Szalai