The win not only moves them above struggling Motherwell but also St Mirren, although all three clubs are separated by goal difference only.
County needed just 11 minutes to break the deadlock at Firhill where Craig Curran was in the right place to tap home from close range.
However, the early goal spurred the hosts into action with Partick dominating the remainder of the first half in terms of chances created.
But the closest they came to grabbing an equaliser came via the lively Ryan Stevenson who struck a post in the 37th minute.
County missed a great opportunity to double their advantage early in the second half when the visitors failed from the penalty spot.
After Danny Seaborne had fouled Liam Boyce, Curran’s spot kick on 53 was brilliantly saved by Paul Gallacher.
But 12 minutes later County did extend their lead as Raffaele de Vita located the bottom right-hand corner of the net from 12 yards after latching on to Michael Gardyne’s assist.
Lyle Taylor pulled a goal back for Thistle on 68 with a close range header from Kallum Higginbotham’s corner.
But back came County who regained their two-goal advantage when Marcus Fraser netted from a tight angle in the 71st minute.