McNulty saw a second-half penalty saved by County keeper Nathan Baxter as they sought to make the game safe, but that was quickly rendered moot when Adam Jackson netted a towering header in the dying embers.
Hibs made four changes from the side that swept aside BSC Glasgow in the Scottish Cup on Sunday, with Lewis Stevenson and Steven Whittaker both rested entirely and Stephane Omeonga and Daryl Horgan dropping to the bench.
Adam Jackson, Vykintas Slivka, Joe Newell and Scott Allan were drafted into the XI. Melker Hallberg had been due to play but was taken ill on the morning of the match.
Ross County, meanwhile, brought in Keith Watson to replace Callum Morris in the only change from their 2-0 triumph against Livingston a week prior.
Hibs exploded out of the blocks, with Martin Boyle smashing over the bar from close range before Doidge stung the palms of Baxter from just inside the box.
The hosts deservedly broke the deadlock after seven minutes when Allan sent McNulty scampering through on goal. Baxter made a rash decision to race from his line, allowing the Scotland striker to clinically fire home his fourth goal in two games from all of 30 yards.
County, backed by 156 hardy souls who braved Storm Ciara to make the journey from Dingwall, came close when Iain Vigurs produced a neat exchange of passes with Lee Erwin and forced a fine low block from Ofir Marciano.
Chelsea loan keeper Baxter bounced back from his earlier error to produce a sharp save to deny Doidge after the big striker had wriggled free on the edge of the penalty area.
However, as has been the case so often in recent months, the Welshman could not be denied a 16th goal of the season. He doubled Hibs' advantage on the cusp of half-time when he met a Newell corner and bulleted a terrific diving header beyond Baxter.
Hibs had a great chance to end any lingering doubt about the result when Marcus Fraser handled a McNulty cross in the box, prompting referee Steven McLean to point to the spot.
However, Baxter plunged to his left-hand side to save McNulty's tame spot-kick.
That only proved to be a temporary reprieve. From the resulting Newell delivery, Jackson towered above the statuesque County defence to head home Hibs' third.