After shipping two first-half goals in September’s 5-0 defeat to Bayern, Bremen were determined to provide greater resistance from the outset of the return fixture at the Allianz Arena.
The visitors managed to negotiate their way to the break without any damage despite seeing the leaders threaten on a number of occasions.
Jamal Musiala’s deft shot was kept out by the alert Michael Zetterer, before Kingsley Coman and Michael Olise curled their respective efforts over the crossbar.
Harry Kane then saw his flicked header drift agonisingly wide in the final act of a frustrating first period for the Bavarians, leaving Kompany with a Bremen-shaped conundrum to solve at the half-time interval.
As is often the case, Kane proved to be the answer to Bayern’s problems, finding the breakthrough from the penalty spot less than 10 minutes after he crashed a thunderous effort against the woodwork.
The England captain drove his spot-kick into the bottom left corner to score his 20th league goal of the season after Bremen defender Anthony Jung was penalised for a handball infringement.
Not content with their slender advantage, the Bavarians went in search of the insurance of a second goal, with Dayot Upamecano drawing a superb reaction save from Zetterer at the near post.
Ole Werner’s charges fought valiantly to stay within arm’s reach of their hosts until their hopes of salvaging a point were quashed by two substitutes.
Konrad Laimer produced an inch-perfect ball for Leroy Sané to guide the ball in at the far post to register his sixth league goal of the season.
Bremen and Jung’s evening took another turn for the worse when the defender gave away another spot-kick in stoppage time.
Unsurprisingly, the ever-reliable Kane slotted home from 12 yards to maintain his 100% penalty record and pile the pressure on second-placed Bayer Leverkusen, who will have the chance to respond in Saturday’s clash with Wolfsburg, while European-chasing Bremen remain in eighth position.
Flashscore Man of the Match: Harry Kane (Bayern Munich)