But Bayern dominated the second half, with Kane scoring his second just after the hour mark, and the Bundesliga leaders could have stretched their lead further.
Alejandro Garnacho, who could make his return to Old Trafford on Saturday, was introduced for Pedro Neto on 68 minutes but could not help the Londoners find a way back into the game.
Palmer, on his 100th appearance for Chelsea, thought he’d scored again late on, but his effort was deemed to have been scored from an offside position, following a VAR review.
The 23-year-old, who missed the Blues’ Premier League victories over West Ham and Fulham, appeared to be clutching his groin towards the end of the game, but Maresca believes he will be fine.