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.
Frankfurt had taken a 14th-minute lead through Marco Russ but saw their advantage wiped out almost immediately as 17-year-old Timo Werner equalised for the hosts.
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.
Both sides squandered good chances to win the game after the break, with Gelson Fernandes and Matthias Ginter missing the best openings for the hosts.
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