The Dons were reduced to 10 men with seven minutes remaining when Mark Kerr was sent off for an apparent head-butt on home skipper Rob Jones, who was also booked for his part in the tussle.
However, it was the Easter Road side's failure to convert the opportunities which fell to Derek Riordan, Colin Nish and Steven Fletcher which prevented them from racking up a third consecutive victory.
Fletcher was perhaps the biggest culprit as he completely missed his volley with the goal gaping in a second half largely dominated by the home team against visitors looking to recover from their midweek Scottish Cup exit to Dunfermline.
The draw maintained the four-point gap between the teams and kept Hibs in the top six and in the hunt for a Europa League place.
Aberdeen, eager to build confidence after their shock quarter-final defeat, emerged with a three-man defence designed to restrict any early opportunities.
However, the home side carved out a pair of half chances within the first six minutes as Aberdeen were forced to clear Alan O'Brien's cross and Fletcher just failed to reach Nish's centre on the break.
It was then Aberdeen's turn to threaten twice in the space of three minutes.
Jamie Smith's corner picked out the run of Zander Diamond in the 11th minute but the defender's poked shot was held at the second attempt by Hibs keeper Grzegorz Szamotulski.
Two minutes later, Richard Foster's cross from deep was met by Tommy Wright but the striker's effort flew just too high.
Both sides looked dangerous going forward and Riordan flashed a shot just wide in the 16th minute before Nish's weak effort wasted excellent interplay from Riordan and Fletcher.
After a lull around the half-hour mark, Hibs threatened again in the 35th minute.
Nish found space on the left side of the area but his cutback was blocked by the Aberdeen defence when a more pinpoint delivery could have brought a goal.
The home side then had the ball in the net but referee Mike McCurry ruled that Nish had fouled goalkeeper Jamie Langfield in bundling in David Van Zanten's cross.
And there was still time for Langfield to block Fletcher's shot after Nish had broken free on the left in first-half injury-time.
The start of the second half belied the excitement that had gone before, with neither team finding the impetus required to threaten in the final third.
However, Hibs came close to the breakthrough three times in the space of four minutes round the hour mark.
With 57 minutes gone, O'Brien picked out Nish with a cross but Langfield somehow blocked the striker's close-range header.
Only seconds later, another O'Brien cross saw Fletcher head wide before the Scotland international completely missed his volley from Nish's cross with the goal gaping.
Having survived Hibs' pressure, Aberdeen then enjoyed a period of sustained possession in and around the home goal without managing to carve out a clear sight of the target.
And as they went down to 10 men with Kerr's dismissal, the Dons were forced to contain wave after wave of Hibs attacks.
As the game drew to a close Langfield dropped the ball under pressure from Jones but recovered in time to block Riordan's follow-up effort.