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Mario Gotze scored twice as 10-man Bayern Munich won at Hamburg to leave the hosts facing the prospect of relegation from the Bundesliga for the first time in their history.

Gotze tapped home the opener before Thomas Muller turned in a second.

Muller set-up Gotze to slot in Bayern's third and, though Hakan Calhanoglu pulled one back for Hamburg, Claudio Pizarro's overhead kick made it 4-1.

Bayern's Jerome Boateng was sent off late on for striking Kerem Demirbay.

Pep Guardiola's Bayern had long since wrapped up the Bundesliga title but it was a welcome result for the former Barcelona boss, following the heavy 4-0 defeat to Real Madrid in the Champions League semi-final in midweek.

Defeat for Hamburg leaves them in danger of losing their Bundesliga status for the first time in their history.

They are two places and two points above bottom of the table in 16th - the relegation play-off place - and cannot finish any higher with 15th-place Stuttgart five points ahead of Hamburg with one game remaining.

That means next weekend will determine who out of Hamburg, Nuremberg and Eintracht Braunschweig finish in the bottom two and who gets the chance to retain their Bundesliga status.

The side that finishes third from bottom will play a two-legged play-off against the third-placed side in the second division, currently Greuther Fuerth.