The Perth side went 2-0 up thanks to goals either side of the interval from Michael O'Halloran and Steven MacLean. Jake Jervis pulled one back for County before the hour mark with a bullet header but Saints held on for the points.
Ross can count themselves unlucky not to take anything from the match, though, after having a fair share of possession throughout.
Saints, who were knocked out of Europe by Spartak Trnava in midweek, threatened first in the sixth minute when David Wotherspoon slipped the ball through for MacLean but before he could pull the trigger County defender Scott Boyd stepped in to clear the danger.
At the other end a Tim Dreesen flick on fell for Filip Kiss inside the box but his shot was charged down.
Then a good run down the left by Graham Carey ended with a decent ball into the box but Saints' defender Tom Scobbie headed clear before Richard Brittain could pounce.
County were back on the attack in the 21st minute and almost took the lead when Yoann Arquin got on the end of a Carey free-kick but his goal-bound shot was blocked on the line. The ball rebounded to Dreesen whose effort was also blocked in front of goal, before a third attempt by Jervis was tipped over the bar by Saints goalkeeper Alan Mannus.
The next opportunity fell to Saints after they won a free-kick in a dangerous position in the 25th minute, but Wotherspoon's effort flew narrowly over.
Dreesen was the first name in referee Kevin Clancy's book for a wild tackle on MacLean.
But just when it looked as if County were getting on top Saints took the lead in the 31st minute.
Antonio Reguero could only get a weak punch on a Wotherspoon cross and when the ball broke out to David Mackay his ball into the danger area was swept home by O'Halloran.
County tried to hit back and they came agonisingly close to an equaliser in the 38th minute when Carey ran at the Saints' defence and his shot to the near post was brilliantly touched onto the crossbar by Mannus.
Saints made the perfect start to the second half by doubling their lead.
Scott Brown fired a ball into the penalty area and MacLean was first to react with a diving header which beat Reguero.
County pushed forward in search of something and an Arquin cross was palmed away by Mannus.
But the home side were thrown a lifeline in the 55th minute when a deep cross from Arquin was met by Jarvis who climbed at the back post to head home.
County had another chance eight minutes later when Jervis knocked the ball back for Kiss but his shot flew well over the crossbar.
There were strong claims for a penalty when Jervis appeared to be bundled to the ground by Scobbie but play was waved on.
County kept pushing forward but the Saints defence held firm with Mannus outstanding in goal.