Germany's World Cup final hero opened the scoring after eight minutes at the Allianz Arena and doubled his tally in the second half, easing the frustration of Saturday's 0-0 draw at Hamburg and extending Bayern's unbeaten start to the campaign.
And the 22-year-old, who made a big-money switch to the Bundesliga champions from Borussia Dortmund in July last year, is loving life under Pep Guardiola at Bayern.
"It was about time that I scored again - especially after all the chances I had," he said. "We could definitely have scored one or two more goals. I think we played well - we owed that to ourselves after the game against Hamburg.
"It was clear to see today that we had fun playing football again and it worked well. I feel great and am happy to be playing.
"It's just so much fun playing with this team and this coach. If you're fit and healthy then everything else happens automatically."
Bayern head to Cologne on Saturday before returning to UEFA Champions League action with a trip to Moscow to take on CSKA in midweek.
