Advantage from first leg
The German side entered the return leg with confidence following their comfortable 4-1 victory in the first leg in Glasgow.
Early shock goal
Stuttgart were stunned less than a minute into the match when Luke McEwan scored to give the Scottish visitors the lead.
Progress despite defeat
However, the early goal failed to inspire a comeback from Celtic, who were unable to score again. Stuttgart held firm to secure their place in the round of 16.
Possible next opponents
Stuttgart will now face either Porto or Braga, depending on the outcome of Friday’s draw.