The Polish striker, who moved to the Allianz Arena from Borussia Dortmund in the summer, opened his account after only 10 minutes with a close-range finish.
But Bayern, for whom new signing Xabi Alonso made his debut in midfield, could not add to their tally and were pegged back by Eric Maxim Choupo-Moting's 62nd-minute leveller.
It left Bayer Leverkusen as the only team with two wins from two after they scored four second-half goals to win 4-2 at home to Hertha Berlin.
They had to come from behind twice, Tin Jedvaj's own goal putting Hertha ahead 24 minutes before he equalised five minutes after the break.
Julian Schieber's third goal of the season restored the visitors' advantage, but goals from Emir Spahic, Julian Brandt and Karim Bellarabi turned the match on its head.
Paderborn picked up their first ever Bundesliga win by embarrassing Hamburg 3-0 at the HSV-Arena.
Elias Kachunga, Mario Vrancic and Moritz Stoppelkamp were on target for the Bundesliga newcomers, who turned up the heat on home coach Mirko Slomka.
Cologne won 2-0 at Stuttgart thanks to first-half goals from Yuya Osako and Anthony Ujah to leave the home fans making their discontent known to coach Armin Veh.
Hoffenheim joined Cologne on four points after a 1-1 draw at Werder Bremen. Roberto Firmino put the visitors in front after 19 minutes, but Alejandro Galvez equalised on the hour mark.
Eintracht Frankfurt also made it a win and a draw from their opening two games by clinching a 2-2 result at Wolfsburg.
Naldo gave the hosts the lead early on, but an own goal from Sebastian Jung saw the visitors level within 10 minutes.
Maximilian Arnold thought he had earned the Wolves their first win of the season with just over 10 minutes to go, but Vaclav Kadlec headed an equaliser five minutes from time.