Given half an hour to secure the victory after second-half red cards for Dons duo Maurice Ross and Chris Maguire, John Hughes' men looked unable to break the stalemate at Easter Road.
But substitute Colin Nish scored in the 88th minute before Liam Miller doubled the tally in injury time to send Hibs above Rangers and into second spot, at least until Sunday.
Hibs were unchanged for the fourth straight match after Sol Bamba shrugged off a knee injury.
But Aberdeen manager Mark McGhee made two changes as Maguire came in for Michael Paton and Gary McDonald replaced the injured Peter Pawlett.
Hibs began in confident fashion and Anthony Stokes was offered a chance on four minutes, latching onto a Merouane Zemmama pass, but the striker overran the ball as he raced in on goal.
Zemmama was booked by referee Steven Nicholls for diving as he rode a challenge from Andrew Considine.
Dons centre-half Jerel Ifil was next in trouble, cautioned for fouling Abdessalam Benjelloun, before Zemmama limped off on 16 minutes to be replaced by Kurtis Byrne.
The flurry of cards from Nicholls continued as ex-Rangers full-back Ross was booked for a tackle on Derek Riordan.
Openings were in short supply at either end, but Aberdeen began to grow into the game without testing Graham Stack.
Hibs looked the more dangerous and on 27 minutes Stokes played in Byrne, whose shot was only deflected wide thanks to an excellent saving lunge from Richard Foster.
From Riordan's second corner, Bamba headed into the ground and over Jamie Langfield's bar.
A fine break from the visitors offered them hope, Charlie Mulgrew feeding Maguire on the right whose deep cross almost picked out the sliding Lee Miller at the back post.
Maguire then became the fourth player booked by the 34th minute, again a touch harshly for catching Riordan.
Stokes, chasing a ball over the top from Kevin McBride, had perhaps the best sight of goal four minutes from the break but sliced high and wide before Riordan was the next man booked.
Given Nicholls' handling of proceedings, there was no doubt both teams would not finish with a full quota of players and three minutes after the break it was Aberdeen who were reduced to 10 men.
Ross caught Ian Murray late and was shown a second yellow card.
Hibs took obvious heart and began attacking in droves, with Stokes and Benjelloun soon wasting openings. Riordan then saw a right-footed shot deflected just past as the visitors struggled to stem the tide.
Matters for Aberdeen then turned dramatically worse as Nicholls reduced them to nine men after sending Maguire up the tunnel just beyond the hour mark.
Maguire, already booked, was shown a straight red card for a late lunge on Kevin McBride.
Hughes threw on Nish before Stokes somehow headed over a Riordan free-kick. As Hibs made heavy weather of claiming the elusive goal, Nish was next to head past.
Mark Kerr eased the pressure with a stinging long-range shot that required Stack to tip over.
Dons youngster Fraser Fyvie then departed on a stretcher following an Ian Murray challenge. As tensions increased, Kerr almost chipped Stack but found the top of the net.
Hibs looked to have run out of ideas but they finally broke Aberdeen's resolve two minutes from time thanks to a fine header from Nish.
And Miller applied the gloss in injury time after firing home with the aid of a wicked deflection off Derek Young.