John Rankin gave County the lead in the fourth minute, but Jason Scotland levelled mid-way through the second half. The winner came three minutes later when Kevin Rutkiewicz put through his own goal following a Don Cowie cross.
County made a rousing start to the game and a defensive error let Alex Burke in on goal in the first minute, but Kevin Cuthbert saved with his feet then Cowie was denied by the Saints keeper when he had two shots blocked.
The goal was only delayed by three minutes when a sweeping ball from Cowie caught out the Saints defence and John Rankin took a touch before drilling the ball past Cuthbert.
Cowie sent in another dangerous cross in the seventh minute which Cuthbert did well to tip over, and the home side should have gone further ahead five minutes later when a reverse pass from Rankin found Winters wide on the left but his cross was missed by Fergus Tiernan with the goal gaping.
It was all County and Cuthbert came to the visitors rescue again when he denied Rankin from close range.
County's Alex Burke missed a sitter when a poor pass back from Kevin James set him free on goal, but after rounding Cuthbert he dallied on the ball and his shot was cleared for a corner.
Saints made a more positive start to the second half and John Henry was only inches away from getting the killer touch on a Simon Mensing delivery at the far post.
The visitors were enjoying their best spell in the game, and the pressure paid off in the 65th minute when Jason Scotland scored when he back-headed the ball into the net following a Kevin James knock-on.
But County restored their lead three minutes later when a good run and cross from Cowie was turned into his own net at the near post by Rutkiewicz.
Saints player manager Owen Coyle almost grabbed a dramatic equaliser in injury time when he hit the ball against the inside of the post and the ball ran out for a goal kick.