The game looked destined for penalties until Steven Saunders rose to nod home a late winner.
James Penrice delivered a perfect corner allowing Saunders to leap above his marker and send a downward header beyond Ross Laidlaw to the delight of the home support.
A dreadful first half was defined by two corners that almost led to goals for each side. Joe Cardle's dangerous in-swinging delivery was a nightmare to deal with and Joe Chalmers inadvertently headed against his own bar after 11 minutes.
County seemed to target former goalkeeper Scott Fox from set-pieces and they were almost rewarded on 19 minutes. Fox flapped at Chalmers' delivery and Ross Draper headed towards goal but Shea Gordon cleared excellently off the line.
County should have been ahead after 42 minutes when Blair Spittal was released through on goal by Billy McKay but he blazed over.
Spittal was Thislte's player of the year last season and he came back to haunt the Jags on the hour. Saunders could only clear a cross to Spittal on the edge of the area and he controlled the ball majestically before arrowing a stunning shot past Fox to give the visitors the lead.
The hosts struggled to respond to going behind and only an excellent diving save by Fox kept out Michael Garydne's curling strike on 74 minutes.
County looked comfortable until Thistle equalised through Kenny Miller after 80 minutes. Alex Jones went on a rampaging run down the right-hand side, breaking into the box before cutting the ball back for the veteran striker to fire home from six yards out.
The wind was causing havoc at Firhill as County repeatedly failed to clear their lines and they were almost punished as Jones fired just wide.
The game entered extra-time and Thistle went ahead through academy graduate Penrice. After Miller was unceremoniously cleared out by Liam Fontaine, Penrice stepped up and curled a beautiful free-kick beyond Laidlaw via the post.
County refused to give up and equalised after 105 minutes. Substitute Harry Paton galloped down the left before firing an excellent low shot across Fox into the net before Saunders won it.