Miller is congratulated on his penalty, giving the Dons a 2-1 lead
Aberdeen recovered from being a goal behind to deliver a blow to Hibernian's hopes of Uefa Cup qualification.
Dean Shiels pounced on 54 minutes to lash the ball beyond keeper Jamie Langfield before substitute Darren Mackie levelled from close range.
Thierry Gathuessi gave away a penalty for the second week in a row, with a foul on Lee Miller, who fired home from the spot to put the Dons in front.
Gathuessi and team-mate Colin Nish were then sent off for dissent.
Defeat meant Hibs missed a chance to take advantage of the draw between Motherwell and Dundee United and are now two points behind Well, who have two games in hand.
Aberdeen's Chris Maguire missed an empty net from six yards after only four minutes. Miller played it across from the left and, with the goal gaping, Maguire put his shot wide.
Hibs striker Abdessalam Benjelloun fired a left-foot shot from a tight angle that Langfield struggled to contain.
Soon, though, Aberdeen exerted pressure on Andy McNeil's goal.
Miller twice went close with headers, the latter effort being cleared off the line after the Dons striker had connected with Alan Maybury's fine cross.
Aberdeen were seeking a victory following the dramatic defeat by Queen of the South in the Scottish Cup semi-final and the 1-0 league loss to Celtic.
Maguire replaced Jeffrey de Visscher from the starting 11 at Celtic Park.
The visitors had captain Rob Jones back in the team after suspension, but hesitancy and nervousness haunted the Hibs central defence throughout the match.
Abdessalam Benjelloun and Felipe Morais made their way into the starting line-up at the expense of Abderraouf Zarabi and Nish.
But the absence of Merouane Zemmama, out with a broken bone in his foot, was keenly felt by Mixu Paatelainen's men.
Shiels is congratulated after giving Hibs a 1-0 lead
The Moroccan has offered pace and trickery to Hibs in recent weeks and, without him, the visitors lacked the skill to retain possession and attack meaningfully.
Seconds before half-time, Langfield denied Hibs an ill-deserved lead when he pushed a powerful left-footed Benjelloun shot round the post.
The second half was a far more exciting affair.
Shiels' 10th goal of the season had the travelling fans dreaming of Uefa Cup football next season, but Mackie equalised within seconds of coming on as a substitute for Maguire with over an hour on the clock.
Having conceded a penalty against Dundee United last week, Gathuessi did likewise at Pittodrie.
Stuart Dougal judged that he had fouled Miller and the striker slotted the penalty home to put the Dons 2-1 ahead.
No doubt frustrated at the penalty decision, Gathuessi fouled Miller in the following minute, for which he was cautioned.
As the Cameroonian protested further, Dougal showed him the red card, damaging Hibs' chances of playing European football next season.
Incredibly, Nish, having played only eight minutes of the match, was also sent off.
Dougal entered his name in his book for a crude challenge on Dons defender Zander Diamond and, when Nish contested the booking, he too was shown the red card.
Hibs were down to nine men and were unable to snatch an equaliser in the remaining 10 minutes of the match.
Aberdeen: Langfield, Maybury, Diamond, Considine, Foster, Young (Walker 68), Nicholson, Severin (Touzani 86), Duff, Miller, Maguire (Mackie 62). Subs Not Used: Soutar, Lovell, Bus, De Visscher.
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