Two goals in the space of five first-half minutes gave Tommy Wright's side the advantage and two more followed in the second period as they cruised home.
Nigel Hasselbaink scored the opening goal after 14 minutes when he converted with a back heel via the post after Saints midfielder Murray Davidson had beaten two defenders before crossing from the byline.
The home side soon doubled their advantage, David Wotherspoon curling a free-kick over the wall and into the top corner.
County finally began to show and went close with a couple of set-pieces but they failed to find the target.
Instead it was St Johnstone who missed out on another goal as they wasted a penalty after Ben Gordon had fouled Wotherspoon in the penalty area.
Wotherspoon took the spot-kick himself but his weak attempt was easily saved by County keeper Mark Brown as he dived to his left and May smashed the rebound over the crossbar.
Hasselbaink then put Davidson clean through as Saints continued to pile on the pressure only for Davidson to drag his shot wide under pressure from Steven Ross.
Stevie May added a third seven minutes after the restart, the striker cutting inside on the edge of the box before driving home left-footed from 12 yards.
Skipper Dave Mackay then killed the game off on 65 when he drilled home a free-kick, with Frazer Wright volleying wide five minutes later after Wotherspoon had found him at the back post.