Brewster capitalised on one of the worst ever professional goalkeeping displays from Hibs' Yves Makaba-Makalamby to put the Dons in charge, but as they sat back on their lead Hibs punished them.
Sub Dean Shiels made the difference as he came off the bench to create Hibs' second and then he pounced for a late equaliser.
Hibs were off to a whirlwind start and had the ball in the net after three minutes when David Murphy ran on to Alan O'Brien's pass to fire home but Murphy had strayed offside.
But the home fans only had to wait 60 seconds for Hibs to hit the front. Both Alexander Diamond and Andrew Considine got in a terrible muddle and Merouane Zemmama nipped in to fire Hibs in front.
It took a great tackle from Murphy to deny Brewster after Guillaume Beuzelin was caught in possession, but it was end to end action with Brian Kerr inches away from 25 yards in reply.
Hibs were hit by a double blow after 17 minutes. Firstly the defence went to sleep allowing Brewster to pick up Michael Hart's cross and slot home a close-range half-volley.
Then influential left-back Murphy was forced off with a shoulder injury.
However if Hibs' defending was bad for Aberdeen's first goal it was simply comical for the second.
Jackie McNamara floated in a free-kick that Makaba-Makalamby charged off his line to collect. He got nowhere near it and the ball bounced through his legs for Brewster to complete a simple tap-in.
On the stroke of half-time Hibs almost levelled when Rob Jones met Zemmama's corner but headed narrowly wide.
The Dons were gifted a third goal 12 minutes into the second half and again it was a terrible error from Hibs Belgian keeper Makaba-Makalamby.
Barry Nicholson's harmless cross from the right was missed completely by the keeper and Jamie Smith had the easiest task to nod the ball into the empty net.
But Hibs found a life-line when substitutes Shiels and Abdessalam Benjelloun combined to set up Steven Fletcher for a 12-yard volley.
And the home side had chances to equalise through Fletcher and Kerr before Shiels was the Hibs hero seven minutes from time.
The substitute took Fletcher's pass and skipped around Derek Soutar to level things up.