Connor Randall was sent off in the 79th minute, but Hibs could not find a way through despite creating the better chances.
The Staggies made six changes, including handing a debut to on-loan Celtic goalkeeper Ross Doohan, while Hibernian rang the changes after their Betfred Cup victory at Forfar last Tuesday, swapping out nine of their starting line-up.
Hibs were inches away from opening the scoring with just five minutes on the clock when Kyle Magennis hit a post.
Martin Boyle then got in behind the defence – as he regularly would throughout the afternoon – to find himself one-on-one with Doohan, only to drag his shot wide of the mark.
It was a dominant spell for the visitors, who then saw Kevin Nisbet denied by a goal-line clearance by Alex Iacovitti.
County began to grow into the game from there as proceedings settled down, but although there were some nice passing exchanges, clear-cut chances remained few and far between.
Michael Gardyne looked to be the most likely to find the net, first shooting wide and then electing to tee-up Charlie Lakin when it looked like he had time and space to pick his spot.
With most of the shots on goal being off target, it took until the 67th minute before either goalkeeper was seriously tested when Doohan denied both Christian Doidge and Nisbet.
Doohan was forced into action again shortly afterwards from Stevie Mallan's shot on goal, but going into the latter stages of the match it was anyone's game to win.
The Staggies were reduced to 10 men in the 79th minute, though, when Randall was shown a red card.
Hibs were attempting to counter-attack and launched the ball over the top for Boyle to run onto, but Randall misjudged the flight of the ball and instead took the Hibs player down.
Referee Nick Walsh deemed him to be the last man, and with Randall having made no attempt to play the ball, he was left with no option but to send the right-back off.
Ross County then naturally went defensive to try and see out the point, and without too much time to make the most of their man advantage they returned down the A9 with only a point to show for their efforts.