Benjelloun scored from the spot after Zander Diamond was adjudged to have handled Alan Gow’s cross.
Anthony Stokes had earlier pulled one back for the home team after first-half goals from Michael Paton and Steven MacLean had given the visitors a two-goal advantage.
Hibs struggled to get their passing game going in the early exchanges and it was Aberdeen who were more satisfied with their opening.
With 17 minutes on the clock, Hibs had the ball in the net when Stokes rifled in Liam Miller’s pass but the striker was adjudged to have strayed offside.
Two minutes later, home manager John Hughes had to be spoken to by referee Craig Thomson after speaking out of turn on the touchline.
Hibernian then carved out their best opportunity of the opening period from a free-kick.
Sol Bamba managed to redirect John Rankin’s set-piece into a crowded goalmouth but Dons goalkeeper Jamie Langfield got across to block Ian Murray’s right-foot effort.
However, it was then the visitors who made the breakthrough in the 24th minute.
Charlie Mulgrew’s long free-kick was knocked on by McDonald and Paton stretched out his leg to divert the ball past a stunned Graeme Smith.
Both sides had to survive penalty claims which were more in hope than anything else.
First, Derek Riordan appealed as his progress into the box was halted by what he thought had been Mark Kerr’s outstretched arm.
Then, at the other end, goalscorer Paton went down after the slightest of touches from the covering David Wotherspoon.
Only a minute later, however, Aberdeen were two goals to the good.
Paton sent in a speculative shot which recent signing MacLean got his head to and the ball looped over a bemused looking Smith.
Hughes reacted to his side’s first-half showing by withdrawing defensive midfielder Kevin McBride and introducing attacker Merouane Zemmama.
However, it was Aberdeen who threatened first after the interval when free-kick specialist Mulgrew curled his shot from a set-piece over the bar in the 48th minute.
Zemmama’s first involvement saw the little Moroccan earn his side a corner after 49 minutes and from his delivery a ricochet from Bamba spun agonisingly over the bar.
A minute later, however, Hibs were back in the game.
Riordan’s long ball was flicked on by Colin Nish and Stokes’ early shot caught out Langfield on its way to the back of the net.
The home side had their tails up but Miller miscued his shot from the edge of the box as the hard-pressed Dons defence hung on.
Bamba almost got a touch to Riordan’s corner and then Nish denied the defender a free header as his own nod down was held on the line by Langfield.
Hibs went with a five-man attack as they brought on striker Benjelloun for full-back David Wotherspoon with 19 minutes remaining.
The pressure almost paid off in the 75th minute but Riordan was twice denied by blocks in the Dons defence before being removed in favour of recent signing Alan Gow.
It was Aberdeen who almost grabbed the next goal when Paton surged inside a couple of challenges and crashed his shot off the underside of the crossbar with Smith well beaten.
Substitute Stuart Duff then beat the offside trap and Smith 30 yards out but his left-footed shot was weak and the chance was wasted.
They were left to rue the missed opportunity as Hibs equalised with only three minutes remaining.
Diamond made his error and Benjelloun netted from the spot to complete a superb comeback.