Some wasteful finishing from Hibs saw them finish the first half goalless after passing up a series of excellent chances to break the deadlock.
Chris Killen was the first Hibs player to spurn a gilt-edged opportunity after eight minutes. He beat Dons goalkeeper Jamie Langfield with a neat right-footed lob but saw his effort drift agonisingly wide of the right post.
Guillaume Beuzelin then went close for the Easter Road outfit but failed to hit the target when well placed.
Despite their superiority, Hibs failed to force a save from Langfield until midway through the opening period. Killen's header was only parried by the keeper and Ian Sproule contrived to fire the rebound wide of target from 12 yards.
Hibs continued to push for a goal after the break but new skipper Rob Jones and Beuzelin both sent efforts wide of target.
The Dons introduced former Caley manager Craig Brewster as a second-half substitute, but the veteran striker failed to make an impact as the game petered out into a goalless draw.