With the scores level going into stoppage time, Ibrahima Traore was fouled inside the area to give the 29-year-old Ibisevic the chance to win the match from the spot.
However, the Bosnia-Herzegovina international skewed his effort high and wide of Kevin Trapp's goal to ensure the points were shared.
Werner's strike made him the youngest-ever goalscorer for Stuttgart and the third youngest in Bundesliga history.
Meanwhile, Freiburg's search for their first win of the campaign goes on after they were held to a 1-1 home draw by Hertha Berlin.
Admir Mehmedi broke the offside trap to open the scoring for Christian Streich's side in the sixth minute - his third goal of the season - but Hertha equalised just before the break.
Ronny's long throw-in was not dealt with by the Freiburg defence and Per Ciljan Skjelbred ghosted in at the back post to level for the visitors.
