Harry Kane had become the first English player to score in his Bundesliga first two games after getting a brace against Augsburg on Sunday.
The first goal came in the 32nd minute, when Leroy Sane fired a shot that bounced off the post, hit Uduokhai and went into the net.
Referee Sascha Stegemann then awarded a penalty for Niklas Dorsch’s handball after being called to check his monitor by the Video Assistant Referee and Kane stepped up for Bayern.
He did not lose, making it two goals up for Bayern.
In the 69th minute, Kane made it three, after Alphonso Davies found him onside and free in the middle to play a calm finish into the net.
After the match, The England Captain had something to say to his supporters, “To score two goals in front of your fans was a special feeling.
“Lots of improvement still to come but to start the season with two wins is a really great start, so thanks for the support as always.
“You know [I] appreciate every single one of you there in the stadium singing my name, so look forward to next week now, recover well and let’s keep it going.”
Kane has now scored in his last seven league appearances, stretching back to his time in the Premier League at Spurs.