A goal by James Keatings in the 63rd minute - moments after Blues had made a raft of substitutions - gave the Scottish Championship side the edge.
Blues by and large dictated the pattern of play but were unable to find that killer instinct where it mattered in the final third.
Hibs were bright and quick on the counter attack and as the game opened out in the minutes either side of the goal, it could have gone either way.
Blues - playing 4-2-3-1 initially- controlled possession for long stretches of the match, comfortably in fact, on a slippy Easter Road surface.
But in the opening period - and as it transpired thereafter - it was a case of making that count.
In the third minute a nice interchange between Jonathan Grounds and Jacques Maghoma saw the latter curl in a dangerous cross that was flicked away off the head of Viv Solomon-Otabor by an excellent clearing header by Callum Crane.
Blues, with Stephen Gleeson and Robert Tesche pulling the strings, continued to dominate without ever really threatening to put their hosts to the sword.
Hibs came close around the half-hour mark, first from a corner.
Despite Ryan Shotton being cleared out by a push, Liam Fontaine got his head on the ball and Tomasz Kuszczak had to make a sharp reaction shot low down.
Then Hibs broke on Blues and Dan Carmichael ran into the space on the right before slipping a pass inside to Alex Harris.
He got the ball out of his feet quickly to create an appealing angle only to then scuffed his attempt towards the bottom corner, allowing Kuszczak an easy gather.
Otherwise it was an uneventful first-half. Matters perked up more after the break.
In the 51st minute Blues constructed a pleasant move from the left that finished when Tesche fed Gleeson and he in turn clipped a ball behind the centre-halves for Clayton Donaldson who, after taking it on his chest, managed a rather awkward looking lob attempt that drifted over.
Next, a brilliant, searching 45-yard diagonal pass by Shotton arrowed over Aaron Dunsmore and put Maghoma in, to the left of the area.
However, he didn't strike through the ball cleanly enough as the full-back scrambled at his shoulder and the chance went across the face of goal and off target.
Hibs responded with a fierce shot from Martin Boyle from just outside the area that deflected off Shotton's shins and flew just beyond the top corner.
A downward header by Keatings, from a left wing cross, bounced not too far away from the post, although Kuszczak had it covered.
Boyle then let rip with a 20-yarder that thudded off the advertising hoardings, at which point Gary Rowett altered things.
He made five substitutions in one fell swoop, sending on Paul Robinson, David Davis, James Vaughan, Paul Caddis and Andrew Shinnie.
That heralded a switch to a diamond formation for the remaining half-an-hour.
But before Blues could settle, Hibs promptly took the lead.
Keatings received the ball deep in Blues area, near the right byline, and twisted away to fire a superb shot into the top far corner from a tight angle.
Stung, Blues increased the tempo and urgency in search of an equaliser.
They should have had a penalty when Shinnie - playing at the tip of the diamond - stepped past Alex Harris on the left of the area and went tumbling over an outstretched leg.
As Shinnie sat on the turf with his hands out in disbelief as the referee waved play on, Hibs broke and almost stole a second.
A deep right wing cross was met on the full by Boyle and his header speared down and hit the crossbar on its way over.
There was another scare from a free-kick delivered low into the thick of it when Jordan Forster stuck out his leg and deflected the ball just wide of the far post.
Inside the final 10 minutes a swift attack set up a half-chance for Vaughan, from Donaldson's pass, but he hurried a low shot through a defender's legs and wide from the edge of the area.
Then, after skilful work from Reece Brown, Blues looked set to have found a way in.
Brown executed two give-and-gos before angling a short pass diagonally behind the defence for Donaldson who turned it on target, first time. But Otso Virtanen, rushing from his line and spreading himself, got a touch on Donaldson's clip and the ball just cleared the crossbar.
But it wasn't to be for Blues, their frustrations summed up when Shinnie did the hard work to take a chip into the area, fend off a couple of challenges only for his attempted set-up for Vaughan to be intercepted.
Blues: Kuszczak, Spector, Grounds, Shotton (Caddis 61), Morrison (Robinson 61), Tesce (Davis 61),
Gleeson, Solomon-Otabor (Vaughan 61), Fabbrini (Shinnie 61), Maghoma (Brown 73), Donaldson
(Arthur 83). Not used: Legzdins, Cogley.
Hibernian: Virtanen, Dunsmore, Crane, Forster, Fontaine (Hanlon 63), Martin, Harris, Stanton,
Keatings, Carmichael (Cummings 72), Boyle (Insall 83). Not used: Laidlaw, McGeough, Allen.