Zdravko Kuzmanovic equalized after gathering a pass from Pavel Pogrebnyak from the top of the area in the 79th minute before swerving a powerful shot into the top of goal.
Sevilla had mostly backed off after Jesus Navas had scored in the 14th minute at Ramon Sanchez Pizjuan Stadium.
Navas, who is hoping for a first call-up for Spain next week, charged into the area to meet Ndri Romaric’s through pass and slot it under goalkeeper Jens Lehman.
Sevilla dropped its first points in Group G to stay top with 10 points, while Stuttgart has three. Unirea Urziceni drew 1-1 with Rangers to sit second with five points while the Scottish club has two points.
Holding a 1-0 lead, Sevilla allowed Stuttgart to create opportunities, with Arthur Boka forcing Javi Varas into a save at the near post in the 36th.
Varas couldn’t reach Kuzmanovic’s header in the 54th, but it came off the crossbar and the goalkeeper eventually gathered the rebound.
Lehman got down to hold Romaric’s hard drive from far out in the 61st in one of Sevilla’s better second-half chances.
Julian Schieber’s acrobatic volley inside the area flew just wide in the 83rd to leave the Bundesliga side still waiting for its first win in the competition.