Rocco Quinn gave County the lead in the 20th minute with a deflected drive, but Michael Ngoo levelled 11 minutes later.
Hearts got their noses in front when Jamie Walker netted just after the hour mark, but right at the death Vigurs fired home from close range to salvage a point for the hosts.
A dangerous cross from Mihael Kovacevic was headed behind by Marius Zaliukas in the third minute as County started on the front foot.
In the next minutes Billy King set up Jason Holt with a chance just outside the six-yard box, but his shot was blocked by County goalkeeper Mark Brown.
It was end-to-end stuff and, following Hearts' first corner of the game, Zaliukas sent a bullet header just past the upright from Fraser Mullen's delivery.
But it was County who took the lead in the 20th minute. After a Richard Brittain corner on the left, Paul Lawson laid the ball off for Quinn, whose deflected shot wrongfooted Hearts goalkeeper Jamie MacDonald.
Hearts were seeing a lot of the ball and grabbed a deserved equaliser in the 31st minute. On-loan signing Ngoo raced onto a long through-ball from Stevenson, shrugged off the attentions of Grant Munro and slid the ball past Brown.
MacDonald pulled off a fantastic one-handed save from Vigurs as County tried to restore their advantage.
The second half started at a slower tempo, with no efforts on goal until the 57th minute. Lawson found Cooper free on the right with a superb ball and the wide-man cut inside but then fired his shot just wide of MacDonald's right post.
Just when County looked to be getting the upper hand, though, Hearts took the lead, when Mullen swung over a cross from the right and Walker stooped to head into the corner of the net from six yards.
It was mostly County at this stage, but, in a breakaway move, Stevenson found himself though on goal only for Brown to produce a low save to his left to keep it out.
But, in stoppage time, Vigurs grabbed an equaliser when he was first to react after MacDonald could only parry a Boyd shot.