But Alex Iacovitti's leveller kept County just a point above their opponents in the table.
Killie started brightly and were rewarded early on as Burke scored his ninth league goal of the campaign.
He volleyed home from just inside the penalty box, leaving the Ross County goalkeeper Ross Laidlaw with little chance, to give the hosts a third-minute lead.
County responded just two minutes later when a knock down by Billy Mckay was collected by Gardyne and the ex-Killie man showed great composure to cut inside on his left foot and fire home past keeper Colin Doyle at his near post.
Pinnock brought the delivery down, turned and finished well on the half volley just inside the area for his second goal in three games.
Kilmarnock pushed for a third. Burke gathered possession in the middle of the County half and carried the ball into space before firing a tame shot down the throat of Laidlaw on his weaker left side.
County went close to levelling the scoring before the break when Gardyne received the ball on the right and again cut on to his left foot, but this time he fired narrowly wide of Doyle's left-hand post.
The visitors remained in the ascendancy after half-time. Good work by Carl Tremarco saw his left-footed cross headed on to the post by Jordan White, with keeper Doyle beaten.
The pressure finally told when captain Vigurs fired in another teasing dead ball, this time from a corner, and centre-back Iacovitti rose highest to head County level once again.
Both sides went in search for a winner and White almost pouncing on a mistake from Arsenal loanee Zech Medley but his shot from an angle was comfortably saved by Killie goalkeeper Doyle.