Defensive lapses looked to have heaped pressure on manager Mixu Paatelainen as his team headed for a third consecutive defeat.
Captain Rob Jones' first-half mistake allowed Darren Mackie the simplest of openers and Zander Diamond's header eight minutes after the interval looked to have sealed all three points for Aberdeen.
However, Jones gave his team some hope and set up a grandstand finish when he pulled a goal back in the 62nd minute.
Despite throwing everything at the Dons in a tense finale, time looked to be running out on Hibs before Fletcher popped up to finally snatch a point.
After five alterations in midweek, Paatelainen made just two changes following the 2-0 defeat to high-flying Dundee United at Tannadice.
Jones, who was left out on Wednesday for family reasons, and striker Steven Fletcher, who missed out with an ankle injury, were drafted in at the expense of Colin Nish and Joe Keenan and both played a major part in their side's comeback.
It was the home side, who went into the match without a win in their last five outings and having suffered back-to-back defeats, made most of the running in the opening exchanges.
In the sixth minute, Scott Severin was forced to make a desperate block on Jones' shot and then John Rankin failed to get the necessary connection on Steven Fletcher's near-post cross before Hibs came within a whisker of the lead a minute later.
Dean Shiels dropped into the 'hole' behind his strikers and ran at the Aberdeen defence before slipping a magnificent pass into the path of Derek Riordan.
However, the former Celtic player's left-foot shot hit the outside of Jamie Langfield's right-hand post and went wide.
Langfield was called into action in the 24th minute as this time he dived to his left to turn Shiels' drive round his post.
Six minutes short of the interval it was Aberdeen who took the lead as the result of a massive mistake in the Hibs rearguard.
Aluko's free-kick should have been easily dealt with but Jones pulled out of a header and left it for keeper Andrew McNeil, only to see Mackie nod in from only six yards out.
And only nine minutes after the break Hibs conceded another poor goal to give themselves an uphill struggle.
Aluko's corner was allowed to proceed unhindered into the six-yard box where Diamond powered in to head home.
A shell-shocked Hibs almost responded immediately but Shiels' penetrating run finished with Langfield blocking the midfielder's eventual shot at his near post.
Fletcher's backward header from Riordan's subsequent corner slipped over the crossbar and then Ian Murray's surging run saw him take the ball round Langfield but fail to get the ball into the goalmouth from a tight angle.
However, the home side finally got a goal back in the 62nd minute and it was a moment of personal redemption for Jones.
The defender rose highest to meet Riordan's corner and Langfield could do nothing about his header.
Hibs sent on winger Alan O'Brien with 18 minutes remaining and he almost created an equaliser two minutes later, surging to the byline and sending a cross to the back post for Fletcher but Langfield blocked his header on the line.
The home side were throwing everything at Aberdeen in search of an equaliser and Riordan came close to giving his team parity in the 79th minute but his snap-shot screwed just wide of Langfield's right-hand post.
With eight minutes remaining of a frantic finale Aberdeen could have wrapped up the three points as Langfield's clearance caught the home side on the break with only O'Brien back.
Aluko withstood his opponent's desperate, mis-timed tackle when he could have looked for a penalty and McNeil blocked his eventual shot.
Then in injury time, after Ricky Foster had blocked Riordan's close-range shot, Hibs finally found an equaliser.
Rankin's shot was deflected into a crowded goalmouth and when Sol Bamba's effort had been blocked Fletcher bundled the ball in from a yard.