Vidal, a Chile international teammate of Sanchez, has won the Bundesliga twice in consecutive seasons at Bayern.
Marc Bartra said returning to action after the bomb attack on the Borussia Dortmund team bus represented one of the "best moments" of his career.
Daniel Ginczek set up three goals and scored the fourth for Stuttgart as the 2007 Bundesliga champions finished with 69 points.
Retiring Philip Lahm and Xabi Alonso said goodbye to the Bayern Munich fans at their Bundesliga title party.
Thomas Tuchel praised the courage of his Dortmund side after their late winner in a thrilling match with Werder Bremen.
Pierre-Emerick Aubameyang's two goals on the final day of the season saw him beat Robert Lewandowski to finish as the Bundesliga's top scorer.