Harry Kane
Darmstadt took the lead through Tim Skarke before Jamal Musiala levelled.
Kane’s diving header put Bayern in front and Musiala dribbled past the Darmstadt defence for his second.
Substitute Serge Gnabry and Mathys Tel made it five for Bayern with Oscar Vilhelmsson scoring Darmstadt’s second.
Despite being bottom of the table, Darmstadt gave Bayern a few scares in the first half but tired in the second period as Bayern exerted their control.
There was one moment of concern for England captain Kane in the second half when he appeared to injure his ankle colliding with a goalpost.
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Kane was substituted after the incident in the 82nd minute and Bayern boss Thomas Tuchel was unsure how serious it was.
“He slipped and fell into the net and twisted his ankle,” said Tuchel. “He’s cooling it down with ice and we don’t have a diagnosis yet.
“When Harry goes off it’s never a good sign because Harry never goes off when there’s still goals to score.”
Kane had previously scored 30 goals in two Premier League seasons while at Tottenham Hotspur.
He has also set a new record for the most goals in a Bundesliga debut campaign, overtaking the previous record set by Uwe Seeler (30) for Hamburg in 1963-64 – which was the first season of the Bundesliga.
He will return to England for the Champions League quarter-finals next month when Bayern face his old foes Arsenal – he has scored 14 goals against the Gunners in 19 appearances.
The first leg takes place at Emirates Stadium on 9 April with the return leg a week later on 17 April.
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