Thistle looked to be on course for victory thanks to James Craigen’s close-range finish, but Philip Roberts’ speculative effort in the 90th minute deflected off Balatoni to leave Scott Gallacher wrong-footed in the Thistle goal.
The home side forged the first chance as Kallum Higginbotham slipped Craigen through on goal but the Thistle man could not find a way past Dundee ‘keeper Kyle Letheren.
The ball broke to Greg Stewart in the Partick area but the Dundee forward was not able to keep his shot on target from 14 yards, while Gary Irvine also went close for the visiting side having nicked the ball off Higginbotham to create the opening.
Ryan Stevenson then created some space out wide in the 58th minute and when he played the ball across, Craigen made no mistake from eight yards.
Craigen was teed up by Higginbotham on the edge of the box but the Thistle midfielder could not find the necessary composure to grab a second goal.
Gary Fraser had another chance to ease the home fans’ nerves but could not take it and the Firhill faithful’s fears proved to be justified with Balatoni’s late, fateful intervention.