Kane capitalised on some non-existent marking to double the lead early in the second half, but Maeda's close-range header gives the travelling Celtic fans at least a touch of optimism ahead of next Tuesday's second leg.
Celtic struggled to make any inroads in the first half and the one time they looked to have caught Bayern on the break, Maeda could not spot Kuhn in space and veered the opposite way.
Celtic had a swift chance to respond when Arne Engels cut the ball back to Reo Hatate in space on the edge of the box, but the Japan midfielder lacked conviction with his shot, which was blocked in the goalmouth.
Celtic were back under pressure immediately after the interval and Kane was somehow completely unmarked when he volleyed home Joshua Kimmich's deep corner in the 49th minute.
The home side almost got a lifeline after a lengthy VAR check and review of Upamecano's penalty-box challenge on Engels, but Spanish referee Jesus Gil Manzano ultimately awarded a drop ball after studying footage.
