The league leaders saw their team bus run out of fuel on the way to the Weserstadion, but had no issues hitting top gear themselves in a comfortable victory.
Arjen Robben and Franck Ribery joined the suspended Xabi Alonso on the sidelines after picking up knocks in the 7-0 UEFA Champions League thrashing of Shakhtar in midweek, while Pepe Reina made his full Bayern debut in goal in place of the rested Manuel Neuer.
Despite those absentees Reina had very little to do in his bow for the Bavarians, who took the lead in the 24th minute through Thomas Muller's curling strike.
David Alaba netted Bayern's 100th goal in all competitions this season in the final minute of the first half with a superb set-piece.
Following their transport issues, Bayern were then forced to wait for kick-off as ground staff attended to a hole in one of the nets.
Once action did begin Pep Guardiola's side struggled to get going in the early stages.
But the visitors would have taken the lead in the 15th minute had Raphael Wolf not sprung brilliantly to his left to turn Lewandowksi's close-range header over the crossbar.
Werder found it difficult to break down the Bayern defence, yet they almost pulled one back in spectacular fashion, with Reina forced to tip over from Fin Bartels' long-range effort with the outside of his boot.
Werder's sense of misfortune will have doubled when Lewandowski nodded home from Muller's cross after the Germany forward had beaten Wolf to a wonderful ball over the top from Jerome Boateng in the 76th minute.
Germany's World Cup-winning captain Philipp Lahm came on for his first appearance since November in the 82nd minute.
