The Dons opened the scoring after 59 minutes when Peter Pawlett was adjudged to have been brought down by Ivan Sproule in the box and Vernon slotted home from the spot.
However, the main talking point of the match came after 67 minutes when Pawlett was shown a straight red card for a challenge on Lewis Stevenson, much to the fury of the home support.
Despite their numerical disadvantage the Dons held on for the victory which moves them six points clear of Scottish Premier League bottom side Dunfermline.
Rory McArdle stepped in to replace the suspended Andrew Considine for Aberdeen, while Fraser Fyvie and Mohamed Chalali were both handed starts with Youl Mawene, who had been struggling with a knee injury, and Chris Clark dropping to the bench.
Hibs, who were looking to end a run of five league games without a win, were missing Leigh Griffiths who was serving a one-match ban for making a gesture to Rangers fans during last week's 2-0 defeat.
Martin Scott came in to replace the on-loan Wolves striker, while Danny Galbraith started in place of the injured Isaiah Osbourne.
Aberdeen made a promising start with Chalali chipping a delightful ball towards Vernon at the back post after four minutes but Paul Hanlon made a brave clearance with the Englishman ready to pounce.
The Dons were forced to make an early change with only 13 minutes gone when Chalali limped off with an injury and was replaced by youngster Pawlett.
Hibs finally came to life after 16 minutes when Galbraith threaded a perfect pass through to Garry O'Connor but the striker's low drive was well held by Jason Brown in the Aberdeen goal.
McArdle spurned a glorious opportunity to break the deadlock after 22 minutes when Hibs defender David Stephens carelessly nodded a Fyvie free-kick straight into his path but the defender blazed the ball high over the crossbar.
Rob Milsom showed a great turn of pace to get past former Don Michael Hart before finding Rory Fallon in the centre but the New Zealand international was unable to divert his header on target.
The Dons had a lucky escape after 28 minutes when Galbraith's deep free-kick found the unmarked Scott but Brown made a terrific save to keep out the former Ross County player's left-foot volley.
Hibernian made the better start to the second half and were appealing for a penalty when O'Connor went down in the box under pressure from Arnason but referee Craig Thomson waved away the half-hearted protests.
But the Dons had better luck after 59 minutes when Sproule felled Pawlett and this time Thomson did point to the spot and Aberdeen's top scorer Vernon assumed the penalty-taking responsibilities to rolled the ball home for his eighth goal of the season.
The Dons were reduced to 10 men after 67 minutes when Pawlett was shown a straight red card for a sliding challenge on Stevenson.
The Dons opted to bring on another defender with Mawene introduced for the tiring Fallon, while Hibernian introduced an extra attacker with Akpo Sodje replacing Hart.
The visitors pressed for an equaliser in the closing stages, with Sodje in particular denied by a smart stop by Brown, as the Dons held on for maximum points.