Thistle started brightly and their first chance came after only three minutes when Will Snowdon's cross was played back into the six- yard box by Adam Strachan and Juan Ramon Escalas' 10-yard shot was blocked and cleared from danger.
Thistle began to take control of the game and after 12 minutes Strachan brought out the best in County's keeper Colin Stewart with an 18- yard shot. A minute later Thistle were presented with an ideal opportunity to take the lead when Escalas' pass put Jamie Mitchell through with only the keeper to beat, but again Stewart did exceptionally well, forcing the Thistle forward wide and again the chance was lost.
Mitchell had a chance to redeem himself two minutes later when a Gibson corner was flipped on by Ken Milne, but he headed wide from four yards.
Having survived this early pressure County began to make chances of their own, and after 16 minutes Snowdon had to clear a deep cross from his line and six minutes later a Jim Laughlan header seemed goal-bound only for Gibson to again clear off the line.
As the second half began Thistle looked for an early advantage, and after 48 minutes Strachan's 10-yard volley was again brilliantly kept out by Stewart.
County again came back into the game and they had the best of any further chances with John Rankin's shot being tipped on to the post at full stretch by Kenny Arthur after 63 minutes.
As the game drew to an end neither side were able to break the deadlock, but it will be County who will be the happier with the point as Thistle stay in the bottom two.