Thistle had been forced to wait until a 3-1 triumph over Aberdeen in February to secure their first league victory at Firhill last term.
But they got off to a flyer in the Scottish Premiership this time, thanks to strikes from Stuart Bannigan, Gary Fraser and Stephen O'Donnell, and a debut own-goal by Ben Frempah.
Partick's start to the season had been delayed after their opener against Celtic was postponed and they approached this match like a team determined to make up for lost time.
Danny Seaborne was drafted straight into the side after penning a two-year deal on Monday, and there were also debuts for fellow summer signings Ryan Stevenson and Abdul Osman.
County named an unchanged side from the one which lost to St Johnstone at the weekend as they arrived in Glasgow desperate to secure their first points of the season.
Thistle thought they had won a penalty with 18 minutes on the clock when Kallum Higginbotham chased down Tim Dreesen's backpass into the box and appeared to be tripped by goalkeeper Antonio Reguero.
But, instead of pointing to the spot, referee Andrew Dallas produced a yellow card and cautioned Higginbotham for diving.
The home side continued to press for the opener and Fraser collected O'Donnell's cross at the back post, only to see his effort crash off the upright.
At the other end, Jake Jervis raced onto a through-ball from Rocco Quinn but his shot went across the face of goal and past the post.
Thistle had looked more likely to find the back of the net and they edged in front five minutes before the break.
Higginbotham picked out Bannigan with a lovely ball and he picked his spot before lashing beyond the grasp of Reguero from 10 yards.
County passed up two chances to level before half-time when Quinn tried his luck with a point-blank shot that Scott Fox did well to tip just over, before Graham Carey saw his own effort skim the crossbar.
Partick still posed a threat after the break and did not have too long to wait for their second goal of the night.
But it was a moment to forget for Frempah, who was thrown into the action at half-time and netted an own goal just nine minutes into his County debut.
Fraser released O'Donnell down the right flank and his cross into the box caused all sorts of problems for Frempah, who diverted the ball into the back of his own net.
There was no way back for County when Steven Lawless played through Christie Elliott, who squared into the path of Fraser and he slotted low past Reguero with 15 minutes to go.
O'Donnell then put the gloss on the win with an angled drive in injury time.