The home side had the best of the chances at the Tulloch Caledonian Stadium on a night when both teams hit the woodwork.
Billy McKay started brightly in the Caley Thistle attack and he forced Jamie Langfield into a diving save after just seven minutes with the ball heading for the corner of the net, after Marley Watkins had created the chance with a strong run towards the penalty area.
The Inverness striker then flicked the ball on with his head to Aaron Doran before shooting first-time from the edge of the box from the return pass, but this time his effort zipped past the post.
At the other end an Aberdeen free-kick skimmed off the head of Caley Thistle defender Josh Meekings and the ball appeared to be drifting inside the post before Dean Brill threw himself across to save.
The best chance of the opening period came eight minutes before the break though when Peter Pawlett weaved his way past four Inverness defenders and laid a pass in front of Niall McGinn whose shot bounced down from the underside of the bar, before the danger was cleared.
McKay had the last opportunity of the half when Doran threaded a wonderful pass inside Shaleum Logan, but the advancing Langfield closed the space down and blocked the shot with his left leg.
Aberdeen survived another scare on 67 minutes when the marauding Watkins clipped a weighted pass into the box from the right flank and Greg Tansey's half-volley beat Langfied to thunder off the upright, and with McKay set to tap in the rebound Logan took the ball off his toe and cleared for a corner.
McKay was involved again six minutes later when his low drive from the right side of the box tested Langfield.
Aberdeen almost snatched victory with just over a minute remaining when Willo Flood chipped the ball back to the penalty spot for McGinn, but Gary Warren took the pace out of his shot and Brill got down to save.