Off the back of a bright, but ultimately frustrating display at Celtic Park last weekend, Gray called on his players to start quickly back in front of their own fans.
However, they were sloppy from the outset and went behind inside three minutes to Campbell's headed effort.
As the first half progressed, the home side did push up the park and found themselves in decent attacking positions, but were let down by a lack of quality in the final third.
Gayle brought them level in first-half added time though, a timely boost that likely spared boos from the sparse home crowd.
The lack of composure in front of goal continued after the break, with Youan wildly slicing a shot from 12 yards before Joe Newell fired well over the bar.
The game then burst into life on 69 minutes when County defender George Harmon hauled Gayle to the ground inside the box. A penalty was awarded by referee Lloyd Wilson after a lengthy video assistant referee check, but Cadden was denied by the legs of Jack Hamilton in goal.
Youan made no such mistake shortly after though, blasting his spot-kick in off the post after Campbell's shirt was pulled by Ryan Leak.
The French forward then turned provider for Campbell to wrap up Hibs' third league win of the season and haul themselves up the table.
In a match of low quality, Hibs found a way to win, which is something they have struggled to do this term. It is a quality that will provide hope to Gray before they travel to Pittodrie next weekend.