Bayern were confirmed German champions for the 30th time in the club's proud history to maintain their iron-grip on the Bundesliga shield in recent years.
"We have showed that we are the best team in Germany," said Lewandowski.
Lewandowski struck two minutes before the break with a brilliant chest and low strike, but Bayern had to endure a nervy final 11 minutes after teenage left-back Alphonso Davies was sent off for a second yellow card.
At the end of a first 45 minutes dominated by Bremen's dogged defending, Bayern broke through when centre-back Jerome Boateng chipped over the top for Lewandowski to score.
It was the Poland striker's 31st league goal of the season, a career best, keeping him on course to be named the league's top scorer for the fifth time.
Head coach Flick landed the Bundesliga title in his first season in charge having stepped in last November.