Harry Kane headed the winning goal deep into added time to give Bayern Munich a 3-2 win over third-tier Wehen Wiesbaden on Wednesday, avoiding a potential shock first-round exit in the German Cup.

Kane had already scored one penalty and seen another saved by Wiesbaden goalkeeper Florian Stritzel when he leaped to head in Josip Stanisic's cross in the fourth minute of five added on.

"Crazy game ... We had some big, big chances to put the game away, but credit to them, they stuck at it," Kane told broadcaster Sky Sport.

"We know we're not the perfect team yet. We know we've got stuff to work on, and tonight shows that."

Bayern has had some shock cup losses in recent years, and came dangerously close to another after giving up a two-goal lead.

Kane got Bayern started from the penalty spot in the 16th minute after Wiesbaden's Ryan Johansson shoved Bayern fullback Sacha Boey.

It was Kane's 90th Bayern goal in his 99th game in all competitions for the German club, and followed a hattrick against Leipzig in the Bundesliga last week.

Michael Olise made it 2-0 off a loose ball in the 50th minute, but Wiesbaden hit back soon after when Fatih Kaya scored on a rare attack by the host.

Kaya's speed made the difference again when he outpaced Bayern defender Jonathan Tah on another counter to level the score.

Kane had the chance to seal the win with another penalty after he was fouled with a clumsy sliding challenge, but Stritzel saved both the England captain's spotkick and his follow-up header.

As extra time loomed, Stanisic hit a cross from deep and Kane rose above defender Justin Janitzek to head in the winner.

The German Cup has been Bayern's least successful competition in recent years. Since its last win in 2020, Bayern hasn't got past the quarterfinals and has lost in the second round in three of the last five years.

Bayern's win over Wiesbaden was the last of the 32 first-round games. All but one of the 18 Bundesliga teams made it into the second round in the end. Werder Bremen was the exception, beaten by second-tier Arminia Bielefeld, last year's runner-up.

Agencies Via Xinhua