Leroy Sane's second-half goal gave misfiring Bayern Munich a 1-0 victory over visitors Arminia Bielefeld on Saturday to keep the champions top of the Bundesliga, a point ahead of Borussia Dortmund.

Sane broke the deadlock in the 71st minute with a powerful drive after the Bavarians had squandered a bagful of chances, to lift his team to 31 points from 13 games, with next week's opponents Dortmund on 30 after beating VfL Wolfsburg 3-1 earlier in the day.

Following a turbulent few days for Bayern after last week's Bundesliga loss to Augsburg and a string of positive COVID-19 cases among their players, they were desperate to reclaim top spot from Dortmund. But they were frustrated in a dominant first half by Arminia goalkeeper Stefan Ortega, whose series of superb saves kept the visitors in the game.

After the break the Bavarians picked up where they left off and had two early golden chances through Sane and Thomas Mueller. Sane had another good opportunity in the 57th minute with a volley that sailed just wide, but he did not miss in the 71st, rifling in from outside the box from a Mueller pass.

Substitute Serge Gnabry rattled the bar minutes later but it was Sane's goal that meant Bayern set a league record with 102 Bundesliga goals in a calendar year, beating Cologne's mark from 1977.