And though Moritz Hartmann pulled one back before the break – also from the spot – the smaller of the two Bavaria sides were unable to find a leveller.
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Guardiola netted a hat trick of league wins in his reign at Bayern Munich and earned the club a record fourth straight title and 25th of all time, before he leaves for Manchester City this summer. “I want to share this title with Jupp Heynckes as we have achieved something really special by winning four titles in a row”, Josep Guardiola said after lifting his third Bundesliga title in three years.
Pep Guardiola’s men were dumped out of the Champions League in midweek by Atletico Madrid, but they put their European exit behind them to secure their 27th league win of the season.
The Bavarians were similarly dominant in his second season, retaining their league title and again reaching the Champions League’s last four.
The Poland striker opened the scoring with a penalty in the 15th minute and claimed his 29th goal of the season in the half.
The hosts gained momentum and rewarded themselves for their efforts as Stefan Aigner nodded home a corner from Makoto Hasebe with 14 minutes on the clock.
Fourth-placed Borussia Moenchengladbach are set to qualify for next season’s Champions League after their 2-1 comeback win at home to Bayer Leverkusen as Andre Hahn scored both of their goals.
Meanwhile, Dortmund suffered their first league defeat of 2016 as they lost at relegation-threatened Frankfurt, who climbed out of the bottom three.
Costa could and perhaps should have doubled Bayern’s lead midway through the first half when he beat the offside trap and was left with only Ramazan Ozcan to beat, but having rounded the last line of the Ingolstadt defence, he lost his balance slightly and placed his shot wide as he fell to the ground.
Gladbach are on 52 in fourth with Mainz 05, Hertha Berlin and Schalke 04 on 49.
Schalke stay on course for a Europa League place after their 1-1 draw at home to Augsburg while Wolfsburg broke their seven-match winless streak, dating back to March, Luiz Gustavo heading in the only goal in the 1-0 victory over Hamburg.
Stuttgart are in grave danger of joining relegated Hannover after giving up the lead to lose 3-1 at home to Mainz.
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Werder Bremen dropped to 16th, which means a promotion-relegation play-off at the end of the season, after their goalless draw with Cologne.
