Graham Carey gave the away side the lead before Callum Paterson levelled things up for Hearts.
Melvin De Leeuw reinstated County's advantage in the second half but the dismissal of captain Richard Brittain ultimately proved decisive as Stevenson nicked a point for the home side.
Ross County looked more threatening in the opening stages with Kevin Luckassen, Gary Glen and Leeuw all having efforts on goal in the first ten minutes that failed to trouble Jamie MacDonald.
And the away side got their reward on 22 minutes when the ball fell to Carey. The Irish midfielder showed great composure to calmly slot the ball into left corner of the net past the outstretched arms of MacDonald.
The goal seemed to spring struggling Hearts into action who managed to get themselves back on level terms just five minutes later.
County failed to clear a corner and Paterson was on hand in the area to fire home a low shot into the bottom right corner of the net.
Dylan McGowan then went close for the home side before County's Rocco Quinn rattled the crossbar with a rasping effort from outside the area.
Quinn had a chance to give the away side a deserved lead on the stroke of half-time but he fired his shot straight at MacDonald as the side's went into the break on level terms
County began the second half as they ended the first and they did not have to wait long to take the lead for the second time in the match.
Four minutes after the restart, Glen played the ball through to De Leeuw and the Dutchman made no mistake slamming a left-footed shot into the corner past the sprawling MacDonald to give the away side the lead.
Hearts were given a much-needed boost when Ross County skipper Brittain picked up his second caution of the game reducing the away side to ten men with 27 minutes left to play.
A minute later Jamie Hamill almost got Hearts back on level terms but he fired his shot straight at Mark Brown.
The home side piled on the pressure forcing a succession of corners as they tried to find an equaliser with Stevenson forcing Brown into another save.
Stevenson was not to be denied however when he picked up the ball in the penalty area in the 89th minute. He steadied himself and smashed the ball into the bottom right corner as Hearts snatched a late point.