Steve May's sixth goal of the season since returning to Saints in the summer looked like pushing the Staggies nearer to the drop zone.
But a dramatic late leveller from McKay in the fourth minute of stoppage time rescued a point for the hosts.
The extremely heavy underfoot conditions and the increasingly ploughed up nature of the pitch tested the skills of both teams after referee Colin Steven had given the match the green light.
After just three Premiership wins in the best part of five months the loss of the first goal was the last thing jittery County needed.
St Johnstone on the other hand have transformed their season after propping up the table in the initial stages of the campaign.
Only four defeats in their last 16 top-flight matches has given the Perth side breathing space and a 12-point cushion over bottom side Hearts.
Needing a quick second half goal to restore confidence, County were thwarted in the main by St Johnstone's well organised and sound defending.
Substitute Harry Paton and McKay, in turn, did well to engineer space for themselves but were unable to get shots away.
Staggies skipper Marcus Fraser did better but his long-range effort failed to trouble Clark, flashing wide of the keeper's left hand post instead.
Appearing increasingly anxious as the match progressed, there was a lack of conviction about the home side for all that they spent much of the second period in Saints' half of the pitch.
McKay shaped to give the locals some hope of retrieving the situation in the 78th minute, but his effort, while close, missed to the left of the target.
With the rain pouring down, Saints got lucky late on when Iain Vigurs' cross from the left was spilled by Clark and Jason Kerr hit the loose ball against his own keeper and it rebounded along the goal-line.
But their luck ran out in the 94th minute when McKay finished off a low cross from Mullin from the right from close range.