Bayer were ahead after 13 minutes through Kiessling as he turned home a rebound after a mistake from Stuttgart keeper Bruno Leto.
Stuttgart were level within seven minutes through Ibisevic, who converted a penalty kick after Simon Rolfes fouled Ibrahima Traoré.
Ibisevic doubled his tally on 55 minutes when he met a long cross from Raphael Holzhauser.
Once again the lead did not last long as Kiessling powered home a header from Michael Kadlec free kick to level the scores at 2-2.
Both sides pressed for a winner but had to settle for a point in a frantic finish at the Mercedes Benz Arena.
A battling point for Stuttgart means that they climb out of the Bundesliga relegation zone, while Leverkusen improve to sixth place in the table.