Jesus Navas broke the deadlock after 14 minutes when he latched onto a Luis Fabiano through to hit past the Jens Lehmann.
Eleven minutes from time, Stuttgart's Zdravko Kuzmanovic hit an equalizer with a long-range shot.
Sevilla played the last 15 minutes with a man down after they used all three substitutes and Aldo Duscher had to come off the pitch upon picking up an injury.
In the same group, Rangers drew at Unirea Urziceni 1-1.
The visitors took the lead when Lee McCulloch scored an opener on 79 minutes, and Urziceni's Marius Onofras brought the score level two minutes from time.
Sevilla are now on top with 10 points, five ahead of second-placed Urziceni.
Stuttgart lie third with three points, while Rangers are fourth on a couple of points.