Stokes struck his eighth goal of the season against the run of play five minutes before the break, the home side having been on top for much of the first period.
And the Irishman grabbed his second of the match when he was in the right place to tap home when Colin Nish fired the ball across the face of goal in the 54th minute.
Aberdeen's misery was complete when Lee Miller was shown a straight red card for a tackle from behind on Merouane Zemmama after 82 minutes.
The result lifted third-placed Hibernian 14 points ahead of Mark McGhee's side.
Aberdeen skipper Mark Kerr passed a late fitness test to take his place at the heart of the Dons midfield, while defender Davide Grassi and midfielder Derek Young returned to the starting XI in place of injured duo Maurice Ross and Peter Pawlett.
Striker Darren Mackie was also handed a starting berth with Chris Maguire dropped to the bench.
And with defender Jerel Ifil completing a two-game ban, Charlie Mulgrew deputised alongside Andrew Considine at the centre of a makeshift home defence.
Derek Riordan recovered from sickness to start for Hibs who kept faith with the same line-up that started last weekend's 1-1 draw at Kilmarnock.
Mackie almost gave the Dons the lead in spectacular fashion with a perfectly timed scissor-kick from a Richard Foster cross after eight minutes but Sol Bamba was in the right place to head the goalbound effort clear.
Stokes squandered a great opportunity at the other end three minutes later when he took too long over his shot, allowing Grassi time to block his effort.
Hibernian goalkeeper Yves Ma-Kalambay was called upon to push a Mulgrew free-kick from 35 yards out for a corner as the home side asserted their dominance.
A mis-hit Mackie cross looked to be dipping under the Hibernian crossbar but Ma-Kalambay again demonstrated his agility by pushing the ball over the bar after 27 minutes.
But it was Hibernian who took the lead against the run of play five minutes before the interval when Zemmama threaded an inviting pass into the path of Stokes who darted past Mulgrew before slotting the ball past Jamie Langfield.
Stokes could have profited from confusion in the Dons defence before the break when they failed to deal with a long ball upfield from Ma-Kalambay but the Irishman could only head woefully wide.
Aberdeen signalled their intent to get back on level terms soon after the interval with Richard Foster stinging the palms of Ma-Kalambay with a fierce shot after 48 minutes before Michael Paton shot over a minute later.
But it was the visitors who scored again after 54 minutes when Nish's shot across the face of goal was turned home by Stokes for his second of the match.
The home side could have pulled a goal back almost immediately but Gary McDonald's tame effort was clawed away by Ma-Kalambay before Considine's header was cleared off the line by David Wotherspoon.
Bamba picked up a needless booking when he was cautioned by referee Douglas McDonald after punching the ball into the Aberdeen net from a Riordan cross after 75 minutes.
The Dons introduced Maguire for the tiring Paton after 77 minutes as the home side searched for a lifeline.
But things got worse for the hosts when Lee Miller was shown a straight red card for a tackle from behind on Zemmama with only eight minutes to go.