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Olise's stunning shot in the 45th minute put the German side in front and Kane doubled the lead with a 49t-minute volley at the far post.
The visitors, bidding to reach this year's final to be played in their own Allianz Arena in Munich, had close to 70% possession in the first half but struggled a lot with Celtic's disciplined backline.
Bayern did have a chance through Kane but it took a superb effort from Olise to break the deadlock on the stroke of halftime.
They struck again four minutes after the restart when Kane was left completely unmarked at the far post.
Kane's goal made him the first English player to score 60 goals in UEFA club competitions.
Celtic cut the deficit in the 79th minute thanks to Daizen Maeda's close-range header to inject late drama into the match.
