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Second-half goals from Sheraldo Becker, Kevin Behrens and an own goal from former Union player Genki Haraguchi took the third-placed side to just two points behind Borussia Dortmund and on the run of champions Bayern Munich.
Stuttgart have now won just one of their past 12 games and anchor the table alone with eight matches still to play.
Mainz dealt fifth-placed RB Leipzig a blow in their bid for Champions League football next season, winning 3-0 at the Red Bull Arena. Goals from Marcus Ingvartsen, Ludovic Ajorque and Dominik Kohr took Mainz, who have now won five of their last seven games, to victory.
Leipzig have now lost two straight since their 7-0 Champions League crushing at the hands of Manchester City in March. Freiburg missed a chance to take advantage of Leipzig's loss, drawing 1-1 at home against struggling Hertha Berlin.
