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Stuttgart, surprise runners-up in the Bundesliga last season a year after narrowly avoiding relegation, were sloppy early as underdogs Augsburg looked to reach the semis for just the second time.
Undav put the home side in front after 29 minutes when he played a clever one-two with former Augsburg striker Ermedin Demirovic, before blasting through Keven Schlotterbeck's legs and into goal. Undav, who made his loan from Brighton permanent in the summer, now has 10 goals in 24 games in all competitions.
The victory came after three straight defeats in all competitions for Stuttgart, including Wednesday's 4-1 home loss to PSG which ended their Champions League campaign at the group stage. Three-time winners, Stuttgart last lifted the German Cup in 1997 and have not won a title since the 2006-07 Bundesliga.
