The England captain opened the scoring in the 52nd minute, heading home Michael Olise's in-swinging corner. Just three minutes later, Kane was felled in the box by Dutch shot stopper Kjell Scherpen. The 33-year-old calmly dispatched the spot kick, extending the German champion's lead.
Just after the hour mark, Vincent Kompany's side were reduced to ten men, with Kim given his marching orders for a second bookable offence. It was a harsh decision on the South Korean, who was deemed to have cynically pulled Raul Florucz's shirt.
The Belgian side failed to capitalise on the opening, as Bayern controlled possession taking the sting out of the affair. Kane will rue his missed chance at another hat trick, when referee Rade Obrenovic awarded another penalty after Kamiel Van de Perre handled in his own box. The former Tottenham striker opted for more pace on his second attempt from the spot, lashing the ball against the bar. The Bundesliga's top scorer had bagged the previous eight penalties he'd taken in the 2025-26 season so far.
Despite Kane's miss, Bayern were largely untroubled in their 250th win in Europe's top competition. The win guarantees Bayern's safe passage to the last-16 of the Champions League, as they join Arsenal as the two teams to have secured a top-eight place in the league phase.