Coming into the game 2-1 down from the first leg, Kirby put Chelsea in front early, breaking from midfield and laying the ball off to Sam Kerr before clipping the return pass into the net in the 11th minute.
Sarah Zadrazil put Bayern back in the driving seat in the 29th minute with a world-class strike, picking up a clearance in a central position well outside the box and then smashing the ball in off the underside of the crossbar.
- Hamilton: How Kirby got back to the top
Ji So-Yun wrestled back control for the Londoners two minutes before the break, thumping home the rebound off the wall from her own free kick to set up a pulsating second half.
Harder's header in the 84th minute looked to have sealed the deal but Chelsea still had to survive a late onslaught, with keeper Ann-Katrin Berger making a superb save and captain Magdalena Eriksson clearing the ball off the line.
With Bayern throwing everything forward for a stoppage-time corner, Chelsea cleared the ball and Erin Cuthbert played in Kirby, who broke free from the halfway line to slot the ball into an empty net to secure the victory.
In the day's other semifinal Barcelona beat PSG 2-1 to secure a 3-2 aggregate win, meaning the Women's Champions League will have a first-time winner when the final is decided in Gothenburg on May 16.