With Motherwell's clash against Inverness Caledonian Thistle postponed due to a waterlogged pitch at Fir Park, only the Global Energy Stadium saw action in the top flight.
Although the visitors had the better of possession, it was Derek Adams' side who had more chances on goal.
They had to wait to break the deadlock, however, with Carey's strike coming in the 88th minute.
The 24-year-old was on hand to slide home his third goal of the season after substitute Melvin De Leeuw had capitalised on a mistake in the Saints defence.
Michael Tidser, another County replacement, had a chance to extend his side's lead, but his powerful drive was kept out by Alan Mannus in the St. Johnstone goal.
Victory moves County up to 10th in the Premiership table, above Patrick Thistle, while St. Johnstone remain seventh, two points behind Hibernian.
‘I was close, very close, to managing Liverpool. I thought it was done, but they went for Joe Fagan. From there, nothing worked out and I lost my motivation’: Ex-Real Madrid boss reveals missing out on Anfield job
‘When I proposed to my wife, I made it a condition that she learn the words of Good Old Arsenal, released before when we won the Double. She did it, too’: Arsenal legend stipulation he made his partner over famous 1971 Gunners song
