Substitute Kevin McKinlay pounced with a late leveller as Partick salvaged a 1-1 draw with Partick.
Thistle created the early chances at windswept Firhill as Dundee were forced onto the back foot.
With six minutes gone, Paul Paton unleashed a long-range shot which forced a diving save from Rab Douglas.
At the other end an angled Mickael Antoine-Curier shot flashed wide before Thistle produced a fine move.
Stephen McKeown and Lucas Akins were involved in creating space for the lively Kris Doolan whose goalbound shot had Douglas diving to his left to claw the effort behind.
The home side continued to dominate but Dundee delivered a sucker punch by going ahead in the 37th minute with their first shot on target.
Eddie Malone was the provider with a neat pass to the unmarked Colin McMenamin who calmly rolled the ball through the legs of Jonny Tuffey.
Dundee looked rejuvenated by the strike and almost doubled their lead through a Georgios Efrem shot which Tuffey parried.
Then with nine minutes remaining, Thistle carved out an equaliser when Simon Storey's cross was headed firmly home by Kevin McKinlay.
Dundee pushed for a dramatic winner, but Tuffey produced a superb save from Andrew Shinnie.