The main benefactors were Darren Mackie and Zander Diamond who grabbed the goals that gave Aberdeen the advantage.
But back came Hibs with Rob Jones' header providing the impetus for Fletcher to equalise four minutes into injury time in a thrilling climax.
Individual mistakes cost Hibs dear as Jones gifted the first and Chris Hogg lost Diamond to concede the second, but the home side showed great spirit to roar back for a share of the spoils.
Hibs created the first chance as Jones fired in a half-volley from 15 yards and only a fine block from Diamond denied him.
And it was the home side who looked more dangerous as Fletcher was only inches away from reaching Ian Murray's tantalising cross.
Andrew Considine was only a foot or so too high with a header from Derek Young's corner, but Hibs should have scored after 16 minutes.
Dean Shiels was the architect with a cute reverse pass, but Derek Riordan's first-time shot spun away off the outside of the post.
But the Dons continued to live dangerously and Shiels was given acres of space to fire in a 20-yarder that Jamie Langfield pushed away at full stretch.
Sol Bamba was next to threaten as he powered a header from Riordan's corner over the bar, but as so often happens it was Aberdeen who took the lead against the run of play after 40 minutes.
Sone Aluko's harmless looking free-kick from the right was inexplicably left by Jones leaving Darren Mackie with a free header from six yards which Andrew McNeill could do nothing about.
And only eight minutes into the second half the Dons grabbed a second goal, again aided by schoolboy defending by the Hibs defence.
Aluko sent in a routine corner from the right and Diamond rose unchallenged four yards out to power home a header.
This seemed to stun Hibs into action and Shiels forced a good stop from Langfield with a low shot after a mazy run.
From the corner Fletcher found a yard of space but couldn't keep his header down.
However, Hibs grabbed a lifeline just after the hour and it was Aberdeen's turn to concede a cheap goal. Riordan swung in a dangerous corner and Jones got a touch to glance a header in at the near post.
And substitute Alan O'Brien almost created an equaliser with his first touch as he clipped in a delightful cross that Fletcher headed goalwards at the back post. Langfield did well to block and Scott Severin completed the clearance.
Riordan fired wide from 15 yards, but Aluko had a great chance to wrap things up as he charged clear. O'Brien tried to clip his heels but Aluko stayed up and McNeil saved with his legs.
But in a thrilling finale Bamba stabbed the ball goalwards and Langfield's block fell for Fletcher to scramble the ball home.