With 10 minutes of a lively encounter remaining, Wylde robbed the hesitant Lewis Stevenson to set up Vernon, and the big striker finished brilliantly from the edge of the penalty area.
Wylde secured the points in injury time when the Dons winger shot beyond Ben Williams into the far corner to the delight of the travelling support.
Aberdeen started brightly at Easter Road as Mark Reynolds forced a save from Williams with a header inside the box.
Niall McGinn then took on Scott Robertson, Ryan McGivern and Paul Hanlon before shooting just over the target.
Hibs finally responded towards the end of the first half when Dons keeper Jamie Langfield had to spread himself to deny Paul Heffernan before Liam Craig fired narrowly wide.
Just after the break Aberdeen striker Calvin Zola turned on the edge of the area before rifling a shot past the goal.
And Hibs survived another scare when Peter Pawlett raced clear of James McPake only to be denied by Williams, with the defender getting back to block the rebound from McGinn.
And McGinn blasted over from 15 yards with the goal at his mercy as Aberdeen continued to threaten.
But Hibs also looked dangerous and a net-bound drive from Rowan Vine was blocked by team-mate James Collins.
The home team missed a great chance to level the match when Langfield slipped, but Collins curled his effort past the post.