Dons goalkeeper Jason Brown saved well from Isaiah Osbourne after 25 minutes and Hibs had appeals for a penalty turned down midway through the second half after the ball appeared to hit Dons defender Andrew Considine on the arm.
Mitchel Megginson on the left was a useful outlet for Aberdeen and had an effort saved by Hibs goalkeeper Graham Stack, but the Dons were worthy of a point in an entertaining contest.
After seven losses from the previous 12 home league matches this term and one win in the SPL at Easter Road since last February - September's defeat of St Johnstone - Hibs boss Pat Fenlon will have been content with the clean sheet, with on-loan Wolves defender Matt Doherty key in the defensive effort.
The result saw Aberdeen, who play Queen of the South in a cup replay on Tuesday night, slip outside the top six.
Aberdeen's 1-0 win over Hibs at Pittodrie on December 17 was part of a run of four wins and four draws in nine league games prior to Saturday's contest which propelled them away from relegation danger.
It was form Hibs, who began the day level on points with the Pars at the foot of the standings, were looking to replicate after claiming just a second home win in a year in last week's William Hill Scottish Cup defeat of Kilmarnock.
Hibs began promisingly, with debutant Jorge Claros adding bite in midfield.
Sean O'Hanlon headed over from a corner before David Wotherspoon saw his swerving shot saved by Brown.
A Lewis Stevenson cross from the left had Mark Reynolds scrambling to clear before Hibs tested Brown.
Stevenson combined with Wotherspoon, who freed Osbourne in the area, but the Dons goalkeeper was equal to the low effort.
Megginson's pace down the left was proving menacing as the Dons came into the game.
O'Hanlon had to stretch to turn one cross around the post before another went narrowly behind Vernon.
A Fraser Fyvie cross was then met by Rory McArdle at the back post and the ball fell for Megginson, but Stack got down well to save a ball which had come through a forest of bodies.
Josh Magennis headed straight at Stack from a Megginson cross and Considine headed wide either side of the break.
The hosts sought a response, but had Doherty booked for dissent for disputing a foul on Magennis, after it appeared the Hibs defender had clearly won the ball.
Hibs then might have had a penalty.
Eoin Doyle forced a corner and a Kujabi cross created havoc in the area, with Doherty and O'Connor challenging for a ball which appeared to hit Considine on the arm. Referee Crawford Allan waved away appeals.
Hibs striker Doyle made way for Roy O'Donovan and the Dons swapped Magennis for Mohamed Chalali and Megginson for Darren Mackie as each side looked for a goal.
The move almost immediately had an impact for the visitors with Clark Robertson's deep cross headed back across goal by Ryan Jack, but the ball fell for O'Hanlon to clear.
A diving Reynolds header turned an inswinging Kujabi free-kick over and George Francomb's resulting corner was well directed, but no-one could apply the decisive touch.
Chalali headed a Fyvie corner wide before Robertson was forced off with an apparent knee injury, Youl Mawene coming on.
Mawene blocked a Stevenson drive as Hibs finished on the attack and the match ended level.