Garry O'Connor missed two decent chances as Hibs edged the first half and Martin Scott twice came close after the break.
Aberdeen improved after a first half in which Richard Foster threatened, but substitute Peter Pawlett had a shot cleared off the line as they pushed for a winner.
Hibs remained bottom of the SPL and, although there was little evidence of a mooted protest against manager Colin Calderwood and chairman Rod Petrie, the home side were booed off by a lower-than-average home crowd.
Hibs had some decent possession in the opening period but lacked a final ball and the Dons improved after being over-reliant on the long ball before half-time.
The hosts' search for their first home win in the SPL this season continued, while Aberdeen have now failed to score in six of their seven league games.
Scott and Victor Palsson came into the Hibernian midfield with Ian Murray moving to left-back and Callum Booth dropped to the bench and Matt Thornhill missing out with a groin injury.
Ryan Jack failed to overcome a head knock to retain his place in the Aberdeen team, but Chris Clark returned from injury to replace him.
Hibernian escaped an early penalty claim when Sean O'Hanlon clumsily bundled Scott Vernon over just inside the box, but referee Stevie O'Reilly was unconvinced an offence had taken place.
Aberdeen had the better of the early exchanges but Hibs gradually came into the game and Palsson and Junior Agogo both had headers saved by David Gonzalez.
O'Connor had two good chances for the hosts but he shot weakly at Gonzalez when played into the right channel and completely missed his kick after Ivan Sproule's square ball across the edge of the box.
Aberdeen immediately broke and Richard Foster curled inches over the far top corner after cutting inside Hibs right-back Richie Towell.
Foster stabbed the ball wide from close range after a long throw and soon caused more problems for Hibs with a bursting run straight down the middle.
O'Hanlon slid in to bring him down, earning himself a yellow card, but Foster's free-kick was deflected wide.
Scott drew a diving parry from Gonzalez early in the second half after chesting the ball down and volleying towards the top corner from 30 yards.
But the incident was a rare piece of quality in a scrappy start to the half.
Aberdeen brought on Josh Magennis for the ineffective Clark while Leigh Griffiths was handed his home debut in the 63rd minute with Agogo going off.
Booth also came on for Murray and soon got a shot on target from long range, Gonzalez scooping the ball wide.
Griffiths also had an immediate impact, sending in a dangerous low cross from the left that was missed by everyone in the goalmouth before Scott shot over at the back post.
Pawlett came on for the visitors and soon had a chance when Graham Stack's clearance fell for him 30 yards out with the goalkeeper stranded.
Pawlett aimed for the bottom corner but Paul Hanlon stretched out his leg to divert the shot wide.
Hanlon headed just over at the other end, but the Dons came close to a last-minute winner when Stack stopped a 20-yard strike from Magennis before blocking the rebound from Foster, who was flagged offside anyway.