However, it was Easter Road goalkeeper Ben Williams who was the true hero for the hosts, producing five excellent second-half saves as well as plunging to parry away a late Scott Vernon penalty.
After a turgid first period, Hibs took control of the contest immediately after the interval, with Deegan producing a dipping swerving drive from distance to break the deadlock.
Aberdeen, roared on by a vociferous following from the north, produced a late rally, with Russell Anderson, Scott Vernon, Niall McGinn and Peter Pawlett all coming close, but Williams was in incredible form.
Even better was to follow from the big Englishman as he saved Vernon's spot-kick with six minutes to play - his fourth penalty save this season - after Jonathan Hayes had been clumsily felled by Hibs skipper James McPake.
With both sides lining up with fairly conservative 4-5-1 systems, the early stages were predictably cagey and shorn of clear opportunities. An effort from distance from Maybury which skewed wide was the sum-total of the first-half action, although Clark Robertson flashed a similarly wayward drive over the bar.
Hibs emerged in the second half with far more attacking impetus and, with 49 minutes on the clock, Deegan opened the scoring in stunning fashion, unleashing a ferocious right-footed shot from 30 yards which kissed the underside of the bar and nestled in the net.
Hibs introduced Done for his debut but it was Dons replacement Vernon who almost made a telling contribution. The bustling striker latched on to an Anderson header across the face of goal but saw his effort from point-blank range clawed away.
Williams then made a laudable double-stop, saving a rasping Pawlett drive through a forest of legs with his feet, and managing to regain his balance swiftly enough to block Vernon's headed rebound.
And a man of the match display was crowned on 84 minutes. Hayes' jinking run into the box was cut short by McPake with an industrial shoulder-charge, prompting referee Iain Brines to point to the spot. Vernon stepped up but, once again, there was only one winner in that duel as Williams pushed his effort on to the post.