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.
That allowed Bayern to hit cruise control in the second half, with Robert Lewandowski rounding off routine success with a late double.
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.
The deadlock was broken nine minutes later, though, Muller giving Bayern the lead with a piece of precise finishing.
Muller had been denied by a fine one-on-one save from Wolf after Werder had lost the ball in midfield, but the hosts failed to clear their lines, allowing him to curl the ball beyond the helpless goalkeeper from the edge of the area.
Bayern laboured in their search for a second, but it finally arrived on the stroke of half-time as Alaba bent his expertly placed free-kick into the top corner after Mario Gotze had been fouled by Sebastian Prodl.
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.
Bartels then had the ball in the net moments later, only to see his effort chalked off for an alleged handball by Prodl.
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.
And Bayern were given further cause for celebration when Lewandowski tapped into an empty net following a neat some neat inter-play with Muller.
