Kane moves closer to goals record as Bayern sink Union
Michael Olise also got on the scoresheet as Bundesliga leaders Bayern went 12 clear. Borussia Dortmund can return the gap to nine points with a win at home to Hamburg in Saturday's late game.
Kane's second-half goal took him to 31 goals this campaign -- the same number Union have scored all season -- and 10 short of Robert Lewandowski's mark from 2020-21, with seven games to play.
"It's still possible, I just have to keep doing what I'm doing," Kane told reporters about the record.
"All it takes is a hat-trick or a couple of braces in a row and then it'll look a bit more likely."
Bayern now have 97 goals this season, four short of the best mark set in 1971-72, when Franz Beckenbauer and Gerd Mueller helped the Bavarian giants tear through the Bundesliga.
Coach Vincent Kompany made five changes from the side which thumped Atalanta on Wednesday to set up a Champions League quarter-final clash with Real Madrid, but kept Kane front and centre.
Union had never beaten Bayern in 14 clashes and held out until the 41st minute, when Olise collected a punted Leon Goretzka pass and curled the ball into the top corner.
Gnabry made it two just before the break, knocking in a rebound at the far post.
Kane pirouetted and curled in Bayern's third just after the break, boosting his tally to 48 in 40 games in all competitions this season.
Gnabry was again in the right place to volley in with 67 minutes gone and add gloss to another big Bayern win.
Bayer Leverkusen's top-four hopes took a hit with a 3-3 draw at rock-bottom Heidenheim after leading 2-0 at half-time and 3-2 with five minutes remaining.
The draw leaves Leverkusen sixth, four points behind RB Leipzig, Stuttgart and Hoffenheim, who are all level on 50 points. Stuttgart have a game in hand.
"I'm speechless," goalkeeper Mark Flekken told DAZN. "We talked at half-time about not getting complacent."
Hoping to bounce back from Tuesday's Champions League exit at Arsenal, first-half goals to Malik Tillmann and Patrik Schick had Leverkusen on course for a routine win.
Heidenheim fought back to level the match through a Hennes Behrens goal and a Marvin Pieringer penalty. Schick once again gave Leverkusen the lead with a header but Pieringer levelled things up from a corner with 85 minutes gone.
Justin Njinmah scored the only goal as Werder Bremen won 1-0 at Wolfsburg to push their hosts closer to a first ever Bundesliga relegation.
Second-last with just one victory in the calendar year, 2009 German champions Wolfsburg could be six points from safety if St Pauli beat Freiburg on Sunday.
Elsewhere, Rhine Derby rivals Cologne and Borussia Moenchengladbach played out a 3-3 draw.