The visitors broke the deadlock when a Leigh Griffiths cross was turned into his own net by Mark Reynolds after seven minutes and Sean O'Hanlon doubled when he headed home 10 minutes later.
Aberdeen were much improved in the second half and Scott Vernon pulled a goal back after 53 minutes with a neat finish from close range, but despite a late rally from the hosts, it was Hibs who held on for three vital points.
Aberdeen, looking to bounce back after a 3-0 defeat to Dunfermline, made two changes with Icelandic international Kari Arnason returning and youngster Jamie Masson given a first start with Chris Clark and Mitch Megginson dropping to the bench.
Jamie Langfield, who had earlier in the day signed a new two-year contract, started in goal for the Dons.
Hibernian were without Lewis Stevenson following his red card in the 1-0 defeat to St Mirren on Sunday.
However, Garry O'Connor shrugged off a foot injury to start as Pat Fenlon made three changes with O'Hanlon and Honduran Jorge Claros also drafted in.
Defender James McPake missed out due to a groin injury while striker Eoin Doyle had to be content with a place on the bench.
The Dons looked eager to get revenge for their 2-1 defeat to Hibs in last month's William Hill Scottish Cup semi-final and created the first opening with Vernon unable to divert an enticing Josh Magennis cross on target in the opening minute.
It was the visitors, though, who broke the deadlock when Isaiah Osbourne found Griffiths on the left wing and his menacing pass across the face of goal was turned into his own net by Reynolds.
Hibs could have doubled their advantage soon after but O'Connor was unable to prod home Thomas Soares' cut-back.
But a second goal did arrive after 17 minutes when O'Hanlon rose highest to head home a Griffiths corner, much to the delight of the travelling support.
Hibernian continued to look the more lively with O'Connor seeing his low driven free-kick cleared by the Aberdeen defensive wall before Griffiths curled over from the edge of the area.
The Dons tried to find a route back into the match before the break with Reynolds wildly lashing the ball over the upright from the edge of the box with his weaker right foot and Vernon seeing his downward volley comfortably kept out by Mark Brown.
Hibs should have put the game beyond doubt within five minutes of the restart when George Francomb was played in by Griffiths but the midfielder's shot was well stopped by Langfield.
And they were to rue that miss after 53 minutes when a Fraser Fyvie cross was headed back across goal by Gavin Rae for Vernon to volley the ball high into the roof of the net.
Hibernian made their first change, bringing on Roy O'Donovan for O'Connor as they looked to stem the Aberdeen momentum.
The hosts almost netted a spectacular equaliser when Arnason evaded the challenge of Claros before unleashing a powerful drive which was tipped over the bar by Brown.
The Dons introduced another youngster in Cammy Smith for Fyvie, who had enjoyed a quiet game, while Hibs brought on David Wotherspoon for Francomb.
And the Hibernian substitute should have settled matters with less than 15 minutes remaining when O'Donovan slotted the ball into his path but the midfielder blasted over from only six yards out.
But the miss was not to matter as Fenlon's side held on for maximum points ahead of Monday's bottom of the table clash against Dunfermline.
