Dougie Imrie marked his 50th appearance for Accies with the opener, after Dons forward Chris Maguire was denied from the penalty spot by goalkeeper Tomas Cerny.
But Nick Blackman struck just two minutes after coming off the bench to leave Hamilton nine points adrift ahead of next week's relegation clash with nearest rivals St Mirren.
Hamilton initially made two changes from the side who defeated Hibernian for the visit of the Dons. Cerny recovered from illness to reclaim the gloves from Sean Murdoch, while David Hopkirk started ahead of Ali Crawford, who was named on the bench.
But Simon Mensing presumably pulled up in the warm-up as Accies were forced to make a late change to the team-sheet, drafting Mark McLaughlin into the side.
Aberdeen made just one change from the side who lost to Celtic in the Scottish Cup semi-final, with Michael Paton added to the team and Josh Magennis named among the substitutes.
Hamilton carved out the first real chance when Nigel Hasselbaink surged into the box only for his shot to deflect off Andrew Considine and fall wide.
At the other end, Aberdeen were threatening when Maguire unleashed from 25 yards and Cerny was called into action to push past his left-hand upright.
Accies had another decent opportunity when David Buchanan released Imrie into the box and he squared for Hasselbaink but Considine was first to the ball to clear before the striker could connect in front of goal.
The Dons had the chance to pile on the pressure when they won a free-kick 35 yards out and Cerny was called into action to punch Maguire's swerving effort out of play.
The Hamilton goalkeeper had to react quickly again at the resultant corner to block a bullet header from Considine after he threw himself in front of Robert Milsom's flag-kick.
With half-time fast approaching Imrie's corner broke for Hopkirk but he nodded just over from six yards, before Imrie's swerving 30-yard drive crashed off the crossbar.
Aberdeen were the more dangerous team after the restart and were awarded a penalty after 52 minutes when referee Calum Murray ruled that Steven Smith was fouled in the box by Gary McDonald.
Maguire stepped up for the spot-kick - Aberdeen's fifth against Hamilton this season - but was denied by a great save from Cerny as he produced his third penalty block of the campaign.
Maguire attempted to turn provider when he swept a lovely ball into the path of Scott Vernon in front of goal but McLaughlin came to the rescue on this occasion when he hooked off the line.
Instead, it was Hamilton who grabbed the opener after 64 minutes when Imrie raced onto a pass from Hasselbaink before keeping his cool and slotting past goalkeeper Jamie Langfield.
Langfield was then forced out of the action and replaced by Mark Howard just two minutes later after he was caught on the face by the boot of team-mate Zander Diamond.
Aberdeen replaced Vernon with Blackman after 73 minutes and he grabbed the equaliser just two minutes later.
Maguire supplied the pass, squaring across the face of goal for Blackman to rifle home at the far post and haul the Dons back into the match.
Blackman was then denied his second goal of the day when his shot bounced off Cerny and crashed off the upright as the match ended all-square.