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Borussia Dortmund beat a struggling Stuttgart side 3-1 but Niko Kovac's team collected its 12th win in 13 league games to ensure it became the new league leader on goal difference.

Bayern has never lost at home to Wolfsburg in the Bundesliga and first-half goals from Serge Gnabry - who signed a new contract this week - and Lewandowski set up a comfortable victory at the Allianz Arena on Sunday (AEDT).

After the break James Rodriguez, Thomas Muller and Joshua Kimmich added to the scoreline, with Lewandowski scoring his second, and Bayern got the perfect boost ahead of a Champions League second leg against Liverpool by moving above BVB despite its win.

Lewandowski hit five goals in nine minutes off the bench against Wolfsburg in the 2015-2016 season but he wasted an early chance by failing to control a lofted Muller pass.

Yannick Gerhardt headed Maximilian Arnold's corner over the crossbar, then Bayern took the lead in the 34th minute.

Kimmich's stepovers left Arnold dazzled and Muller pulled the ball back for Gnabry to nudge in from close range, the winger then creating a second goal within three minutes.

A throughball from James found Gnabry and he unselfishly squared for Lewandowski to tap in and pass veteran former Bayern forward Claudio Pizarro on the list of foreign goalscorers.

James scored the third himself in the 52nd minute, beating Koen Casteels with a placed 20-yard finish, the goalkeeper later making a fine save to tip over Muller's drive.

But the Bayern forward would not be denied again in the 76th minute, slotting home Franck Ribery's pass to end a week that saw him dropped from the Germany squad on a high.

And although Dortmund got back in front against Stuttgart, Kimmich and Lewandowski added late headers from Ribery centres to boost Bayern's more impressive goal difference further.