Leandro Trossard has scored two goals in his past two games for Arsenal
Kane, Tottenham's record goalscorer, received a predictably hostile reception from Arsenal's supporters, who saw the Gunners make the perfect start when Bukayo Saka's low finish put them ahead after only 12 minutes.
Bayern belied their poor form in the Bundesliga to turn the game around before the break as former Arsenal forward Serge Gnabry swept home the equaliser six minutes later.
Kane's moment arrived when William Saliba tripped Leroy Sane at the end of a blistering run after 32 minutes. The England captain stepped forward for the resulting penalty and silenced the taunts with his 15th goal in 20 appearances against Arsenal.
Mikel Arteta's side were not at their fluent best but substitute Leandro Trossard was the beneficiary of outstanding work by Gabriel Jesus to equalise.
Arsenal felt they should have had a penalty in the final seconds of stoppage time but the referee waved away their appeals when Saka went down as he was challenged by keeper Manuel Neuer.
The Gunners were arguably also fortunate not to concede a penalty themselves earlier in the half, when Gabriel picked the ball up with his hands after the referee had signalled for a goal-kick to be taken.
Several Bayern players complained at the time but the referee swiftly waved their appeals away.
The second leg in Munich is on Wednesday, 17 April.
-- Courtesy of BBC sport