The visiting team had missed a series of chances with Niall McGinn, Peter Pawlett and Calvin Zola among the villains.
Derek McInnes replaced Zola with Vernon just after the hour-mark and the move paid off in the 79th minute when he drove the ball high past Hibs keeper Ben Williams from the edge of the box.
Wylde, who had come on for Peter Pawlett and set up Vernon for his goal, wrapped up the points with a breakaway effort in the second of four minutes added time with his first goal for Aberdeen since signing for the club in the summer after leaving Bolton.
Pat Fenlon's side were far from their best and deserved no more although substitute James Collins, on for Owain Tudur Jones, missed a great chance presented to him by Dons keeper Jamie Langfield with four minutes remaining.
Hibs, who went into the game having lost only once in their previous nine games, were boosted by the return of skipper James McPake who replaced fellow stopper Michael Nelson who was out after suffering an eye socket injury against Celtic last week.
McInnes who also made one change, bringing in defender Clark Robertson for Andrew Considine, watched his side have the best of the early exchanges.
In the fourth minute Williams made a fine save from Mark Reynolds' drive from distance which was heading into the top corner.
The nervous-looking Easter Road defence had to work hard to withstand the pressure, mostly aerial, exerted by the Dons who took control of the game.
In the 14th minute McGinn embarked on a mazy run from wide on the right leaving three Hibs players in his wake before flashing a left-footed shot from the edge of the box over the bar.
Aberdeen were wasteful with a series of crosses and set-pieces and almost paid for that profligacy in the 33rd minute when Hibees striker Paul Heffernan just failed to get on to a Liam Craig cross, with Langfield cutting out the danger.
Craig fired wide of the target moments later but it confirmed that the Leith side were at last coming into the game.
There was a flurry of activity close to the break.
Three minutes from the interval Zola fired a shot into the side-netting from 12 yards to end another Pittodrie attack in disappointing fashion, before Langfield blocked from Heffernan who had raced on to a Scott Robertson pass, with the Dons surviving the corner.
The men from the Granite City started the second half with renewed vigour and should have scored within four minutes when Pawlett raced clear of the Hibs defence chased by McPake.
However, his shot was brilliantly saved by Williams and when McGinn pounced on the rebound, McPake had got back in position to make a tremendous saving block.
Moments later, McGinn failed to properly connect with a Jonny Hayes cross which allowed Williams to gather his header comfortably and as the visitors dominated, Zola and McGinn failed to hit the target with efforts.
Collins replaced Tudur Jones and Rowan Vine came on for Heffernan as Hibs tried to force their way back into the game.
Zola then made way for Vernon in the 64th minute before Barry Robson replaced Hayes.
They game became increasingly scrappy in the closing stages but when Vernon took a pass from Wylde, he slammed it high past Williams before taking the acclaim of the Red Army behind the goal.
However, those fans held their breath in the 86th minute when Langfield slipped to give the ball straight to Collins but the Hibs substitute curled his shot past the far post.
However, in injury time, Wylde popped up to allay any fears of a late leveller when he drilled the ball past Williams and into the far corner.