Both camps will be satisfied with the result, although Hibernian boss John Collins will feel confident that his side can progress as they now have home advantage.
After a fairly uneventful opening period it was the visitors that passed up the best opportunity of the match in the 16th minute. Dean Shiels got beyond Michael Hart to pull the ball back across the area where Chris Killen was only able to knock the ball wide with the goal gaping.
As the tie opened up Darren Mackie sprinted clear of the Hibs defence on to a Scott Severin pass, but the striker was forced wide by David Murphy and his tame effort from 20 yards was comfortably held by Andrew McNeil.
Aberdeen twice went close in quick succession midway through the half. Gary Dempsey's threaded throughball found Mackie whose driven left-foot effort was parried by McNeil back to the edge of the 18-yard box where the ball was knocked into the path of Barry Nicholson.
He crashed in a great shot, which the young goalkeeper again saved with aplomb. As Aberdeen pressed, a corner kick from Nicholson saw Lee Miller rise above his marker but he couldn't keep his header on target.
As the Dons pressed, Miller was again narrowly off-target when his downward header from a Michael Hart cross fell the wrong side of the post.
Aberdeen keeper James Langfield cost his side dearly in 42 minutes when he failed to hold a long-range effort from Steven Whittaker, the ball falling into the path of Ivan Sproule who had the easiest of tasks to knock his shot into the empty net.
Dons boss Jimmy Calderwood made his intentions clear upon the restart bringing on forwards Craig Brewster and Chris Maguire in place of Andrew Considine and Gary Dempsey, as the home side went with a very attack minded 4-2-4 formation.
Sproule continued to torment the Dons rearguard and, in the 52nd minute, a clever pass from the diminutive wideman sent Shiels clear on the left, where only a last-gasp challenge by skipper Russell Anderson averted the Dons falling two behind.
How vital that intervention proved to be minutes later when a great pass out of defence by Hart sent Mackie flying down the wing. His brilliant cross into the area found the head of Brewster whose downward effort gave keeper McNeil no chance from around eight yards.
The visitors shocked their hosts in the 72nd minute when a driven ball into the area from Murphy was taken on the chest by Killen, before he wheeled to crash the ball home.
The home side pressed to the end and finally got their just rewards with 90 seconds left on the clock.
Severin's hoisted ball into the area was knocked on by Brewster, with the ball falling into the path of Nicholson who gleefully slotted the ball home from eight yards out to bring the sides level again.