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.
Richard Brittain's third corner kick in the sixth minute was headed over the Hearts crossbar by Scott Boyd.
Billy King then set up Jason Holt with a chance just outside the six-yard box, but his shot was blocked by County goalkeeper Mark Brown.
The home goal survived another let-off in the 11th minute when Ryan Stevenson broke free on the left, but his shot across the face of goal flew wide of the far post.
At the other end Vigurs picked up a ball on the edge of the area but he flashed his shot-cum-cross wide of goal.
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 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, who 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-hand post.
Just when County looked to be getting the upper hand, though, Hearts took the lead.
Mullen swung over a cross from the right and Walker stooped to head into the corner of the net from six yards.
County made a double substitution in an effort to get back in the match, with Steffen Wohlfarth and Gary Glen coming on for Sam Morrow and Alex Cooper.
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.
Wohlfarth glanced a header wide of the near post when he got on the end of Evangelos Ikonomou's cross in the 82nd minute, and at the other end Andy Webster forced a sensational fingertip save from Brown.
But, in stoppage time, Vigurs grabbed an equaliser when he was first to react after MacDonald could only parry a Boyd shot.
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