Midfielder Mark Kerr was red carded seven minutes from time after reacting angrily to a challenge from Rob Jones.
The draws means Hibs have managed four league games without losing a goal - their best spell for 18 years.
Aberdeen were without Lee Mair and Darren Mackie due to hamstring injuries and Chris Maguire dropped to the bench following the midweek cup defeat. Gary McDonald, Tommy Wright and Andrew Considine all came in.
Steven Fletcher had a chance for Hibs after only five minutes when Colin Nish skinned Zander Diamond on the left but his strike partner failed to connect with his low cross with the Dons exposed.
Alan O'Brien had a couple of decent breaks down the right but his crossing let him down.
But it took a decent save from Grzegorz Szamotulski to keep Hibs level after 11 minutes. Jamie Smith's corner picked out Diamond and his volley was scrambled away by the goalkeeper at full stretch.
Tommy Wright then headed over from six yards after a precise cross from Richard Foster and the Dons striker took a head knock in the process. It was several minutes before he returned to the action with his head bandaged.
McDonald was then left unguarded at a Charlie Mulgrew free-kick but he steered his 16-yard header well wide.
It was an open game and Hibs immediately had a chance at the other end. Fletcher sent Derek Riordan scurrying clear and his brilliant first touch gave him a shooting chance but he pulled his effort narrowly wide.
Riordan then played in Nish but his shot from the edge of the box lacked any power and Jamie Langfield saved easily.
Fletcher and Nish were linking well and another exchange on the edge of the box gave Fletcher a shooting chance but he could not direct his effort on target.
Hibs made a change in the 28th minute when Ian Murray replaced Lewis Stevenson, who had taken a knock earlier in the game.
Nish thought he had put Hibs ahead two minutes from the break when he bundled in David van Zanten's cross but referee Mike McCurry ruled he had fouled Langfield.
Langfield produced a great one-handed save to deny Fletcher on the stroke of half-time after Nish had cut the ball back.
Hibs started the second half strongly and Fletcher guided a header wide from six yards after good work from O'Brien.
The Hibs striker was then guilty of missing a clear-cut chance when Nish picked him out at the far post but he missed his kick with only Langfield to beat.
Kerr then received his marching orders for squaring up to Jones but it looked a harsh decision.
Hibs could have won it at the end with Langfield saving well from Riordan and was then fortunate to escape when a Rankin shot bounced off him.