Liam Craig gave Saints the lead against the run of play on the half-hour mark and the Perth side went a player down a couple of minutes later when Rowan Vine was sent off for an off the ball incident with Richard Brittain.
County piled on the pressure in the second half and Sam Morrow hit a deserved equaliser in the 68th minute.
But, with the home side pushing for a winner, Saints grabbed a vital second in the 85th minute when Frazer Wright headed home following a corner.
County made a brisk start to the game and Saints goalkeeper Alan Mannus had to look smart to get down to a Rocco Quinn cross before Gary Glen took advantage.
Glen was in the thick of things again three minutes later when the ball fell for him inside the box but his angled drive flew well over the crossbar.
The home side continued to press and Quinn tested Mannus with a long range drive which the goalkeeper managed to smother.
County were knocking the ball about with some confidence in the middle of the park and they carved out another opening in the 17th minute when Quinn whipped in a cross for Morrow - but the forward hooked his shot wide.
Quinn was the supplier again a couple of minutes later with a ball to the far post but Iain Vigurs just failed to get a touch.
In a rare attack former County favourite Gary Miller burst into the 18-yard box but he was crowded out at the vital moment.
The home side were seeing more of the ball but Vine threatened a couple of times down the left with dangerous crosses.
County came close to an opener in the 27th minute when Scott Boyd met a Vigurs inswinging corner but his bullet header flashed inches over.
But Saints took the lead against the run of play when Craig smashed a left foot shot into the corner of the net.
However, the Perth side were reduced to 10 men a couple of minutes later when Vine was shown a straight red card by referee Crawford Allan after the Saints player lashed out on Brittain.
Mihael Kovacevic replaced the injured Ross Tokely at the start of the second half and within a minute Quinn flashed a shot over the crossbar from outside the 18-yard box.
The home side were well on top and a Vigurs cross from the left was missed by Morrow in front of goal before a shot by Kovacevic from the other side was palmed away by Mannus.
At the other end Murray Davidson, who had just come on for Nigel Hasselbaink, thought he had scored when his shot from the edge of the six-yard box crashed off the underside of the crossbar and onto the line but the ball was cleared.
The 10-men continued to look a threat going forward and Gregory Tade turned Boyd 20 yards out and his shot flew narrowly past the upright.
But County eventually got the goal they deserved in the 68th minute when Grant Munro played a one-two with Vigurs on the left and his cross into the box was swept into the net by Morrow.
It was no more than County deserved and they kept the pressure on with a series of attacks.
It was constant pressure from County and McMenamin forced a full length save from Mannus when he looked sure to score.
The County goal had a let off in the 85th minute when Saints' sub Steven MacLean forced Michael Fraser to turn the ball for a corner.
From the Craig's resulting flag-kick, Wright rose above the County defence to head home the winner - and Saints almost went further ahead in injury-time when David McKay cracked one of the inside of the post before it was cleared.