The game ended even more dramatically at the final whistle as Conte and Tuchel were shown red cards for a scuffle.
“It was a deserved defeat. We weren’t good today. We didn’t defend well and lost too many balls,” Bayern Munich coach Julian Nagelsmann said.
Both sides are building towards the World Cup, and the competition will have its group stage drawn on Friday in Doha.
Chelsea said with the win against Lille, that they were geared up for the Carabao Cup final with Liverpool on Sunday.
The game ended 2-1 as Palmeiras defender Luan was shown the red card in added time.
Kai Havertz scored just five minutes after the blast of the whistle, giving the Blues a lead at the Bridge.
Juventus stay top of Group H, while Chelsea are second on the group table with 3 points in from two games.
Chelsea held Liverpool to a 1-1 draw at Anfield in their English Premier League game on Saturday.
With France playing draw against Hungary and Germany defeating Portugal group F looks more dangerous as any of the big three teams could be eliminated in the group stage.
A first half goal by Chelsea’s record signing, Kai Havertz, was enough to deny the Citizens their first champions League trophy.