It took the defending champions only eight minutes to open the scoring, with Xabi Alonso thumping in a volley from just outside the penalty area after a cross was half-cleared.
Bremen's weak resistance was broken again four minutes later when Franck Ribery slipped Lewandowski through on goal and the striker finished superbly from a tight angle.
The dominance continued after the interval when Lewandowski stretched to tap in a Thomas Muller cross, before Philipp Lahm drove in the fourth via the post after more precise passing.
Ribery added a fifth by finishing well from Muller's pass and Lewandowski completed his treble with a late penalty as Bayern won their first league match of the campaign for the fifth year in a row.
Mats Hummels made his second league appearance for Bayern - the first was in May 2007 before his decorated spell with rivals Borussia Dortmund - while Carlo Ancelotti became the first manager to take charge of teams in Europe's top five leagues.
Bayern dominated possession from the first whistle, with Muller having an early shot deflected narrowly wide for a corner, and the opening goal soon arrived.
Lahm's cross was headed straight to Alonso, who teed himself up on the edge of the penalty area and hammered a stunning volley into the top corner.
Muller then forced a fine save from Felix Wiedwald but it was 2-0 to Bayern shortly afterwards.
Lewandowski beat the offside trap to race on to Ribery's throughball into the left channel and, from a narrow angle, the Poland international produced a brilliant curled finish.
Wiedwald denied Lewandowski and Muller shot at the goalkeeper as Bremen failed to put Bayern under pressure, before Muller hit the post from 25 yards and Lewandowski missed the rebound.
Bayern came close again after 38 minutes as they once more cut Bremen apart easily, with Ribery and Muller involved in a sumptuous one-touch move, but Wiedwald got enough on Lewandowski's shot to deflect it on to the crossbar.
Lewandowski had a further first-half opportunity in the 42nd minute after Bremen gave away possession, but Wiedwald made the stop as he continued to keep the score down.
The third goal arrived in the first minute after the interval, as Lewandowski was presented with a simple close-range finish from Muller's superb right-wing centre.
After 65 minutes Bayern scored the fourth goal their dominance deserved to ensure a 14th straight win over Bremen, with Lahm and Muller playing a one-two before the full-back shot across Wiedwald and in off the upright.
Muller was given far too much space to pick out Ribery for a powerful finish and Lewandowski rolled in a penalty for his second hat-trick in two games - he claimed the matchball in the cup thrashing of minnows Carl Zeiss Jena seven days ago - after substitute Rafinha was fouled.
On this evidence Bayern will take some stopping as they aim for a fifth consecutive league title.