The Bayern coach praised his players' control in the first half but admitted the second half turned into "a real test of character" as Union pushed them to the limit.

"We did many things right in the first half, but the second half was a fight," Kompany said. "We defended their set pieces well and were unlucky with the penalty. For me, that was not a penalty on Harry Kane. His arm and the opponent's arm were in the same position. When you go for the ball with momentum, there shouldn't be a penalty. I'm a former defender and I know these situations."

Kompany also stressed Bayern's ambition to return to the capital for the final. "I hope we'll continue and come back to Berlin. These games are part of the journey, and they shape a team," he added.

Kane Leads the Line as Bayern Survive Late Storm

Harry Kane powered in a superb first-half header as Bayern did just enough to advance, but the match swung wildly, with Bayern giving away two penalties and Union scoring two own goals from corners. Union's Leopold Querfeld converted both penalties, keeping the home side in touch throughout a frantic evening.

Bayern, who have won the German Cup a record 20 times, are into the last eight for only the second time in the past six seasons. They travelled to the capital aware that Union were the only side to take a point off them in domestic competition this season, after the sides drew 2-2 in November.

Union's hopes of causing another shock collapsed early when Benedict Hollerbach's attempted clearance from a Joshua Kimmich corner bounced off David Ansah's thigh and into his own net after 12 minutes. Twelve minutes later, Kane rose above his marker to glance in another Kimmich corner.

Union responded when Jonathan Tah was penalised for handball and Querfeld calmly sent Manuel Neuer the wrong way from the spot. However, Bayern restored their two-goal lead just before half-time when Diogo Leite headed a Michael Olise free-kick into his own net.

Kane then conceded a second penalty early in the second half after catching an opponent with his elbow. Querfeld converted again, giving Union renewed belief. The hosts pressed relentlessly, forcing Bayern deep into their own half, but Kompany's side held firm to secure a vital victory.

Stuttgart Progress Despite 'Ugly' Display

Earlier in the evening, defending champions Stuttgart moved into the quarterfinals with a 2-0 win at 10-man Bochum. Philipp Strompf endured a nightmare first half, looping a header into his own net before being sent off shortly before the break.

Deniz Undav continued his outstanding scoring form, heading in early in the second half to take his tally to seven goals in his past four matches. Despite the win, Undav admitted to ARD that he "wasn't satisfied" with the performance. "We played weirdly, we were erratic, but in the cup it only matters if you progress," he said.

Freiburg also advanced with a 2-0 home victory over second-division Darmstadt, with Vincenzo Grifo scoring from the spot and Lucas Hoeler sealing the win. Bayer Leverkusen, St Pauli, RB Leipzig and Hertha Berlin all reached the last eight on Tuesday.

William Gallas: Arsenal made a 'mistake' by signing Kai Havertz