Richard Brittain's second-half penalty ensured the Staggies would be safe from the drop, but Hibs still have work to do in the survival fight after failing to find a leveller at Victoria Park.
The visitors showed plenty of attacking intent in the early stages and Jason Cummings tested Mark Brown in the County goal before Daniel Handling dragged a shot wide.
But the Staggies spurned a decent chance when Yann Songo'o sent a close-range header over the bar and Hibs tried to punish this miss, with Alan Maybury drawing another save from Brown.
Only wayward finishing was preventing Terry Butcher's men from taking the lead and Liam Craig twice went close with headers, glancing wide and nodding over the bar.
But County carried more threat in the second-half as Brittain's header drew a fine save from Ben Williams, who then kept out the midfielder's attempted chip.
Jordan Forster sent a header wide as Hibernian responded well, however, their hard work was undone when Scott Robertson's reckless challenge on Jordan Slew allowed Brittain (63) to fire home from the spot.
Slew remained in the thick of the action, forcing Williams into a brave save after a determined run, but County's lead could have been shortlived as Cummings' drive was inches wide.
The lively Cummings sent a header past the post during Hibs' late push for a leveller, but County clung on for a precious win after Brown kept out Forster's header.