Bayern coach Pep Guardiola dismissed talk of a crisis after the champions drew 1-1 against Schalke on Tuesday following a 4-1 hammering at Wolfsburg, and normal service was resumed by the Bavarian giants at the Mercedes Benz Arena.
The leaders were not at their best against Huub Stevens' strugglers, but Robben took his goal tally to eight in his last nine games and 14 for the season with a fine strike to open the scoring late in the first half.
Defender David Alaba then opened his Bundesliga account for the season with a sublime free-kick, six minutes after the break, to ensure Bayern remain eight points clear of second-placed Wolfsburg, who beat Hoffenheim 3-0.
While Bayern remain on course for yet another title, Stuttgart are now bottom of the table and have secured only five points at home this season.
