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Hoffenheim maintained their bid for a top-four spot thanks to Sebastian Rudy’s late equaliser in a 1-1 draw with Schalke.

Hoffenheim trailed to an early goal from Alessandro Schopf. It was the Austrian midfielder’s seventh goal of the season and also made it three goals in his last three games. However Hoffenheim gradually began to dominate and Kerem Demirbay and Ermin Bicakcic both came close to making things level. Hoffenheim had to wait until the 80th minute for a share of the spoils when Germany midfielder Rudy headed home Steven Zuber’s cross. The draw leaves Hoffenheim fourth, a point above Hertha Berlin, while Schalke climb a place to 12th to sit level on points with Augsburg.

Borussia Monchengladbach backed up their excellent Europa League victory away to Fiorentina on Thursday with a 2-0 victory at struggling Ingolstadt. Captain Lars Stindl and Andre Hahn scored second-half goals as Gladbach made it four wins from five league games.

After a sterile first half which produced few scoring opportunities, the visitors took the lead in controversial fashion on the hour. Stindl turned in a cross at the back post with what appeared to be his head, but television replays showed the ball in fact had come off his hand, much to Ingolstadt’s despair. The hosts chased the equaliser late on but they were punished on the break as Hahn sealed the points in injury time. Monchengladbach’s victory moves them up three places to 10th as Ingolstadt remain struggling in the bottom two ahead of next weekend’s trip to Hoffenheim.

Bayern Munich celebrated head coach Carlo Ancelotti’s 1,000th competitive match in club management with a comprehensive 8-0 thrashing of Hamburg. Arturo Vidal opened the scoring with a powerful drive from the edge of the box before Robert Lewandowski scored twice, the first from the penalty spot, to give Bayern a comfortable 3-0 half-time lead. The Poland striker completed his hat-trick on 54 minutes with a composed finish before David Alaba, two from Kingsley Coman and an Arjen Robben strike sealed a crushing victory over relegation-threatened Hamburg.

RB Leipzig continued their title push after they secured a 3-1 victory against Cologne to stay five points behind leaders Bayern. Emil Forsberg broke the deadlock on five minutes with a calm finish after a weak clearance from Cologne goalkeeper Thomas Kessler fell to Timo Werner, who played in the Sweden international to curl home. An own-goal from Dominic Maroh doubled Leipzig’s lead before the break, but Yuya Osako’s close-range finish halved the deficit six minutes after the restart. Werner’s 13th goal of the season ensured victory as Leipzig maintained their record of being undefeated every time they have scored in the Bundesliga.

Borussia Dortmund won away from home for only the second time in the league since November to stay in third place with a 3-0 win at Freiburg. Papastathopoulos Sokratis headed in Raphael Guerreiro’s free-kick to give the visitors the lead before Pierre-Emerick Aubaumeyang tapped in Marco Reus’ driven cross to double their advantage shortly after the restart. The Gabon striker scored a close-range second to secure victory and keep Dortmund within touching distance of Leipzig in the final automatic Champions League spot.

First-half goals from Stefan Bell and Levin Oztunali helped Mainz move up to 10th in the table after winning 2-0 at Bayer Leverkusen. Defender Bell opened the scoring with a bullet header from Oztunali’s corner on three minutes before the provider turned scorer with a free-kick that deceived everyone and found into the far corner on 11 minutes.

Augsburg added to Darmstadt’s relegation fears with a 2-1 comeback victory. The basement boys broke the deadlock two minutes after half-time through Marcel Heller, but Paul Verhaegh’s penalty and Raul Bobadilla’s chipped finish five minutes from time extended the host’s poor run of form which has seen them pick up just four points from a possible 42.