Thistle eased the pressure on manager Alan Archibald with a 2-1 victory at the Energy Check Stadium at Firhill despite falling behind to Sofien Moussa’s early effort and conceding a first-half penalty.
Ryan Edwards levelled with 15 minutes left and Storey struck a vital goal to draw Thistle level with Kilmarnock on points at the bottom of the table after Moussa had missed a great chance for his second.
Archibald made four changes to the side which lost 2-0 at home to Kilmarnock last week but Dundee started the brighter of the two sides.
Jesse Curran danced through the home side’s defence and his cutback found A-Jay Leitch-Smith whose strike from 10 yards was palmed away by Tomas Cerny.
Dundee continued to press forward with Curran, Leitch-Smith and Moussa causing problems but the home side came close when a Danny Devine header from a Chris Erskine free-kick was met by a smart save from Scott Bain at his near post.
However, Dundee took the lead inside nine minutes. Kevin Holt’s cross from the left found the unmarked Moussa at the back post, and the forward sent a diving header into the empty net.
The visitors were then awarded a penalty in the 22nd minute when Leitch-Smith was brought down after rounding Cerny. However, the goalkeeper redeemed himself instantly by denying Leitch-Smith from 12-yards - doing well to save with his feet in the middle of the goal despite diving to his right.
The visitors took off from where they left off after the interval and continued to cause problems on the counter-attack. The impressive Leitch-Smith had a couple of efforts blocked by the Thistle defence and another just wide of Cerny’s left-hand post.
The introduction of Blair Spittal and Kris Doolan gave the home support a boost as they laboured in search of an equaliser.
The changes eventually paid off. Edwards followed up on Doolan’s blocked effort to bundle the ball home from six yards.
Cerny then stopped the visitors from going back in front with a wonderful save to deny Moussa from point-blank range.
And there was more drama to come as Doolan’s cutback found fellow substitute Storey, who slotted the ball home from six yards.