The home side missed out on the chance to go temporarily top last week when they lost at St Johnstone.
Now Robbie Neilson’s team find themselves five points adrift of Brendan Rodgers’ table-toppers after being frustrated by Jim McIntyre’s County side.
Both sides hit the woodwork but it was County keeper Scott Fox who proved to be the main obstruction to Hearts as he pulled off a string of superb first-half saves.
The visitors were left to play out the last seven minutes a man light after Ian McShane was dismissed for two quick-fire bookings but they clung on to claim the point which sees them overtake Rangers into fifth.
It took 10 minutes of Hearts probing before they were able to find an opening.
Conor Sammon drove 70 yards upfield before slipping in for Tony Watt but Fox denied the Irishman’s strike partner with a reflex save.
Callum Paterson’s failure to clear his lines from Martin Wood’s free-kick at the other end almost cost his side in dear. The right-back made a mess of his header, sending it straight to Staggies skipper Andrew Davies, who thudded a headed attempt of his own off the crossbar.
While the visitors were busy appealing that the ball had crossed the line after bouncing down off the woodwork, the home side quickly countered.
But they were left disappointed as Sammon’s shot was stopped by Fox before Marcus Fraser booted the ball to safety just as Watt raced in for the rebound.
County though were beginning to rely on their number one a little too much, with Fox denying Igor Rossi after he ran free from his marker to meet another Cowie delivery before later standing up well to block Sammon’s effort after the striker was set clean through on goal by Watt.
And it was the upright which came to County’s rescue nine minutes into the second period when Sam Nicholson came close from another swift Hearts breakaway.
Faycal Rherras and Perry Kitchen - who was leading out Hearts for the first time since replacing Alim Ozturk as club captain - both had shots sail over the bar as a sense of desperation began to creep into the Gorgie side’s play.
The County bench was left incensed when Jamie Walker - who has already served a two-game ban for diving this season - appeared to go to ground easily while driving at Michael Gardyne and Paul Quinn but McIntyre was relieved to see the incident prove elementary in the end as Watt blazed the resulting free-kick over.
Hearts were given a late invitation to attack as McShane was issued two bookings by Alan Muir in the space of just three minutes after clattering into both Jamie Walker and Rherras but they could not make the most of their numerical advantage.