Carlo Ancelotti's side really struggled to break through a very tough Bremen defence until two goals in three second half minutes from Lewandowski sealed yet another win for the defending champions.
The win means that Bayern have won both their opening games, while, on the other hand, Bremen suffered their second defeat from two games but can take heart from their performance against Bayern.
The visitors started well but they failed to take their early chances
As expected, Bayern started the game on the front foot and they had a number of chances to open the scoring in the first 15 minutes of the game.
Mats Hummels had the first chance when he found space in the box but he saw his header from a corner kick go just wide of the goal.
Arjen Robben was next to close when he done his trademark move by cutting in from the right-hand side but Jiří Pavlenka was equal to the shot to keep it out of the net.
The third chance of the sequence was the best though when Corentin Tolisso, unluckily for him, hit the crossbar with a volley after Pavlenka dropped the corner kick into his path.
The hosts came extremely close to scoring against the run of play before half-time
After their early pressure though, the visitors took their foot of the gas and that allowed the home side to get some possession of the ball and that almost led to a goal but Ludwig Augustinsson's goalbound effort was cleared off the line by Niklas Süle, who did well to get back on the line.
That chance though was the hosts only chance of the first half as they had to put all their efforts on defending well against the defending champions, who really pushed to try and get the opening goal but it never happened as the sides went in on level terms at the break.
Two goals in three minutes sealed the win late on for the defending champions
The second half was very competitive for the large part as the home more and than held their own against Bayern until a moment of quality opened the game up.
Kingsley Coman, on as a second half substitute, created the first goal of the game when his brilliant cross into the box was flicked into the net by Lewandowski, who showed his true class to score with his first shot on goal.
It was almost two with their next attack when a beautiful chipped pass from Tolisso found Thomas Müller, on as a second half substitute, in on goal but his vollyed effort was brilliantly saved by Pavlenka.
That save only denied the inevitable though as Lewandowski scored his second of the game when Müller gave him the ball and the Polish forward powered hi way into the box before putting the ball into the net under the legs of Pavlenka.
Understandably, after conceding two goals in three minutes, the hosts ran out of steam and that allowed Ancelotti's men to see the game out with much fuss to register two wins from their opening two games.