Goalkeeper Jamie Langfield prevented the visitors falling further behind when he saved Michal Ordos' spot-kick.
Dons keeper Jamie Langfield made smart first-half saves from both Carlos Cuellar and Jean-Claude Darcheville.
Antoine-Curier had an effort saved by Jamie Langfield before the Frenchman struck the opener.
Miller then added some gloss to a nervous victory when his deflected shot deceived goalkeeper Jamie Langfield.
BBC: SPORT | Football | Scottish Premier | Hibernian 2-0 Aberdeen
Samaras then doubled his tally with a fine solo effort, chipping past Jamie Langfield with 15 minutes remaining.
Neither goalkeeper had much to do until Aberdeen's Jamie Langfield made a hash of pass-back, conceding a corner.
Chris Humphrey out-paced Steven Smith to reach a long ball and smashed a shot past Reds goalkeeper Jamie Langfield.
Saints' Graeme Smith kept out an early effort by Michael Paton, but Cillian Sheridan tapped home after Jamie Langfield saved Danny Grainger's shot.
Charlie Mulgrew was dismissed for an alleged head-butt on Kyle Lafferty before Rangers Madjid Bougherra saw red for a challenge on Jamie Langfield.
Dons boss Mark McGhee shuffled his pack following the midweek Scottish Cup defeat, with goalkeeper Jamie Langfield, Sone Aluko and Jerel Ifil dropping out.
Conroy had pointed to the spot after Michael Stewart fell under a challenge from Aberdeen goalkeeper Jamie Langfield, but he then gave a goal-kick.
And substitute McCarthy took advantage of some indecision in the home defence by pouncing to guide the winner past keeper Jamie Langfield after an hour.
Hamilton had the majority of possession in the opening minutes, Easton and Marco Paixao testing Jamie Langfield in the Aberdeen goal with some inventive play.
BBC: Hamilton's David Elebert (left) tussles with Sone Aluko
Andrew Considine was sent off for two bookings and Jamie Langfield made a great late save to deny Brian McLean as the visitors held on.
Eremenko was fouled in the box by keeper Jamie Langfield and Jamie Hamill stroked home the resulting penalty, then Sammon came close again before the end.
Opposite number Jamie Langfield prevented a Lee Mair own goal.
Jamie Langfield saved Miller's penalty to give the Dons hope.
In the same match, which Rangers won 2-1, Dougal also red-carded Madjid Bougherra after the defender caught Aberdeen goalkeeper Jamie Langfield with his boot while challenging for the ball.
Ricardo Vaz Te looked to pounce on early nervousness in that reorganised home rearguard, but he was ruled offside after his powerful effort was saved by goalkeeper Jamie Langfield.
But the Highlanders were almost handed the opening goal when Aberdeen goalkeeper Jamie Langfield's slack clearance landed at the feet of McBain but the midfielder's shot was blocked by Aberdeen captain Scott Severin.
New Zealand international Rory Fallon made his Aberdeen debut while goalkeeper Brown deputised for the unavailable David Gonzalez, with Jamie Langfield on the bench for the first time since suffering a brain seizure during the summer.
And, although Aberdeen made the brighter start, it was the visitors who could have taken an early lead when Enoch Showunmi outmuscled Jerel Ifil, but goalkeeper Jamie Langfield gathered at the feet of the former Leeds striker.
But it was Hibernian who took the lead against the run of play five minutes before the interval when Merouane Zemmama threaded an inviting pass into the path of Stokes, who darted past Mulgrew before slotting the ball past Jamie Langfield.
Raith were gifted an equaliser 14 minutes later when Jamie Langfield, who had endured a nervy start to the match, made a mess of collecting a Stephen Simmons free-kick and the grateful Mole calmly slotted the loose ball past the stranded goalkeeper.
Jamie Langfield, Zander Diamond and Lee Miller are the obvious key men and give a decent spine to the team, while Gary McDonald and Mark Kerr are both going to have to have big seasons, particularly if McGhee adopts his favoured 4-3-3 formation.
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