Kylian Mbappé scored Madrid's goal after the visitors had taken a two-goal lead at the Santiago Bernabeu stadium on Tuesday.
Kane had been listed as a gameday decision after missing the team's Bundesliga match last weekend because of an ankle injury.
The result left Bayern with an edge ahead of the second leg in Germany next week as it tries to reach the Champions League semifinals for the first time since 2023-24.
Arsenal won 1-0 at Sporting Lisbon in the other quarterfinal on Tuesday.
On Wednesday, Barcelona will host Spanish rival Atletico Madrid, and Liverpool will visit defending champion Paris Saint-Germain.
Madrid and Bayern are playing their sixth knockout-stage meeting in 14 seasons, with the Spanish powerhouse having won four of their five two-leg match-ups since the 2011-12 season.
Kane participated in the build up of Bayern's first goal in the 41st minute, exchanging passes with Serge Gnabry who ultimately fed a through ball for Luis Diaz inside the area. The Colombia forward calmly sent a low shot past Madrid goalkeeper Andriy Lunin.
Kane scored himself in the 46th with a nice one-timer from the top of the area, firmly finding the corner with a low strike. It was his 11th Champions League goal, equalling his best scoring season in the European tournament.
In Lisbon, Kai Havertz scored in stoppage time to give Arsenal the win in their first leg quarterfinal.
The substitute fired past goalkeeper Rui Silva from close range at Estadio Jose Alvalade to give Mikel Arteta's team the advantage ahead of next week's second leg at the Emirates.
Havertz settled a tight game of few chances by combining with fellow substitute Gabriel Martinelli.
The German controlled the ball in the box and then side-footed into the net to hand Sporting its first loss at home since August.
"To score a late goal is always nice," Havertz told Amazon Prime. "We will take that result. There is still a lot of work to do next week."
Victory meant Arsenal bounced back from successive defeats which cut its quadruple trophy hunt in half in recent weeks. Losses in the League Cup final and FA Cup quarterfinals had shaken the Premier League leader going into Tuesday's match.
