Dean Shiels capitalised on poor play from Zander Diamond to break the deadlock early in the second half, only for substitute Darren Mackie to equalise within a minute of his introduction and Lee Miller to then score a penalty having been fouled by Thierry Gathuessi.
Another foul on Miller saw Gathuessi booked, before he was sent off for arguing the decision and any hopes of a comeback from Hibs were soon dashed when replacement Colin Nish was dismissed for dissent.
With Aberdeen manager Jimmy Calderwood away on a European scouting mission, his assistant Jimmy Nicholl was left in charge of the home side.
Nicholl came close to seeing the Dons take an early lead when a cross from Barry Nicholson was headed into the path of an unmarked Chris Maguire by Miller.
Maguire looked to have a relatively easy task of scoring at the back post, but decided to take an extra touch and missed while under pressure from Rob Jones.
The response from Hibs saw Abdessalam Benjelloun flash a powerful half-volley across goal which was unconvincingly turned wide by home goalkeeper Jamie Langfield.
Aberdeen were soon on the front foot again and this time Jones had to clear off his own line to prevent Miller's header from an accurate Alan Maybury cross finding the net.
Hibs eventually emerged as an attacking force on the half-hour mark when an ambitious long-range drive from John Rankin fizzed just over Langfield's crossbar.
They improved slightly following that foray forward and did not offer Aberdeen any other goalscoring opportunities during the opening period.
Nevertheless, the Edinburgh club lacked urgency when in possession and did little to concern Langfield until first-half injury time.
In the last notable action before the interval, Felipe Morais flashed in a low shot from the edge of the Aberdeen penalty area that looked destined for the bottom corner of the net, until a faint touch from Langfield carried the ball wide.
Hibs started the second half in far more purposeful fashion and scored the opening goal in the 55th minute when Diamond was punished for losing possession in ruthless fashion by Shiels, who squirmed into the Aberdeen penalty area before supplying a composed finish.
Hibs almost conceded an equaliser shortly afterwards, as Miller's header found Nicholson and his first-time shot was blocked by visiting goalkeeper Andy McNeil.
Play continued to rage from one end to the other, with a Hibs counter-attack providing a sight of goal for Rankin, but the midfielder was denied by Langfield.
The game then took a major swing in Aberdeen's favour with the arrival of Mackie, who scored immediately after replacing Maguire.
Ian Murray and Martin Canning were left in a state of confusion as Mackie wriggled along the byline and the striker restored parity by somehow flicking the ball past McNeil from the tightest of angles.
Aberdeen quickly built on that goal, with a needless foul from Gathuessi on Miller resulting in a penalty that was dispatched with aplomb by the Aberdeen forward.
Any hopes Hibs had of getting back into this game then vanished as Gathuessi and Nish were sent off in a madcap nine-minute spell.
Aberdeen created several chances late on against their beleaguered opponents but could not add to their advantage, with Mackie shooting straight at McNeil when clean through on goal.