Goals from Yoann Arquin and Yann Sango'o in the first half had put County firmly in charge of the game at Rugby Park.
But two second-half goals from Boyd either side of a red card for Filip Kiss saw the home side earn a share of the spoils to the delight of Johnston.
"Overall it was a great point for us after being two goals down," the Kilmarnock manager said.
"The boys showed tremendous character or desire especially, after the game against Celtic in midweek. We dominated the second half and really deserved at least a draw.
"It was two great goals from Kris Boyd and he was the quickest to react and put his face in where it hurts for the second.
"He is a top-quality striker and his goals show how much he means to us."
But Ross County manager Derek Adams was disappointed his side had not made the game safe and felt both of Boyd's goals could well have been disallowed on another day.
"The result was a travesty for football," he said
"Overall we played really well - two up in the first half going on four or five.
"For their first goal Boyd's handled the ball before swivelling to score. For the second he has two hands on the back of our player.
"Added to that the sending-off was very soft and disappointing."
Tempers appeared to flare at the end of the game but Adams was keen play down any spat with his opposite number.
He said: "It is a great testimony to how far we have come that Kilmarnock are so delighted to get a point that Allan Johnston races past my dugout to celebrate."