The Brazilian's 25-yard left-foot shot swerved in off the underside of the bar to send bottom club Darmstadt to a seventh straight defeat.

Bayern laboured for much of the game against spirited opponents.

Peter Niemeyer should have equalised, heading straight at Manuel Neuer, who had parried Jerome Gondorf's free-kick.

Carlo Ancelotti's side regained first place from Leipzig, who had moved three points clear by beating Hertha Berlin 2-0 on Saturday.
 

One eye on Wednesday?

Leipzig have supplanted Borussia Dortmund as Bayern's biggest Bundesliga title rivals this season, and Wednesday's meeting between the two side in Munich is keenly anticipated.

There was a sense that Ancelotti and his players may have had one eye on that fixture, as they were far from at their best against Darmstadt.

Bayern captain Philipp Lahm, who was listed on the team sheet, suffered a problem during the warm-up and was not risked - perhaps with Wednesday in mind - as Rafinha was drafted in to replace him.

There was little fluency about Bayern's play, and Robert Lewandowski - who signed a contract extension lasting until 2021 on Tuesday - did not look like continuing the run that had brought him five goals in his previous three matches.

The closest that the Poland striker came to a goal was a free-kick floated just over the bar towards the end of the first half, on a day when Bayern rarely threatened other than from set-pieces.

There was a degree of encouragement in defeat for Darmstadt, who have struggled to recover from the departure of coach Dirk Schuster for Augsburg during the summer.

Norbert Meier, Schuster's replacement, was sacked on 5 December, but interim coach Ramon Berndroth coaxed an energetic performance from his players, and they would have gained a valuable point but for Costa's unstoppable shot.