James Chambers' ninth-minute strike and a Liam Miller own goal handed bottom of the table Hamilton a 2-0 half-time lead and Accies held on despite Akpo Sodje's 66th-minute strike.
The result, sparked by livewire Nigel Hasselbaink, who laid on the opener, was Hamilton's first win at Easter Road since November 1986 and saw them reduce the deficit at the foot of the table to nine points.
Eighth-placed Hibs had opportunities - Francis Dickoh hit the bar with a header and missed two others - but suffered just a second loss in 10 games.
With five matches remaining, Hamilton will need to continue to show all the battling characteristics which earned them victory today.
They also must end their season-long run without a home win and beat nearest rivals St Mirren on May 1.
Like Accies, Hibs were haunted by the prospect of relegation until a run of five straight wins - including a 2-1 victory at New Douglas Park - lifted Colin Calderwood's side to safety.
Fewer than 100 Hamilton fans made the journey east to Edinburgh, but after nine minutes they had reason to be optimistic that their side could claim a first win at Easter Road since 1987 and enhance their survival prospects.
Hasselbaink, operating alone up front, drifted wide to the left and ran at Francis Dickoh.
The striker, nephew of Jimmy Floyd Hasselbaink, kept running, Dickoh unable to make a tackle, before evading his marker on the byline and cutting the ball back for Chambers to tuck in his first Accies goal.
Hasselbaink then fluffed a good chance after 17 minutes, missing a simple tap-in from Chambers' through ball.
Dickoh almost made amends for his defensive failings, but his header from David Wotherspoon's corner was well saved by Tomas Cerny.
Hibs looked vulnerable in defence but were beginning to make inroads in attack and Dickoh should have equalised but headed Miller's cross from the right over.
Lee Kilday hit the bar with a header from Dougie Imrie's corner, but Accies did go two up after being granted another set-piece opportunity when Sodje fouled Hasselbaink.
Sodje attempted to clear Alistair Crawford's inswinging free-kick with a header which ricocheted back off Miller and dribbled into the net after 34 minutes.
Dickoh then headed onto the bar from Callum Booth's corner, but Hibs faced a two-goal half-time deficit and manager Colin Calderwood replaced Victor Palsson with Martin Scott.
Hibs spent the second half camped in Hamilton's half but struggled to break down the visitors until the 66th minute.
Callum Booth's long cross-field ball found Sodje racing through and he tucked a cool finish beneath Cerny.
Hibs continued to press and Derek Riordan missed a half chance before Cerny scrambled Booth's deflected cross round for a corner.
Hibs continued to press forward and Sodje had a strike which deflected over and from the resulting corner Paul Hanlon twice was denied on the line, Cerny collecting the loose ball.
Hamilton were forced deep to protect their lead and Riordan flashed a shot off target and referee Brian Winter turned down two hopeful Hibs appeals for handball in the area.
Substitute Grant Gillespie cleared a Sodje header off the line before Simon Mensing headed narrowly wide of his own goal from Mark Brown's long ball forward.
Imrie was booked for tangling with Wotherspoon at the edge of area as Riordan stepped up to take a stoppage-time free-kick which was retaken.
Cerny held the shot and Hamilton survived to claim a vital victory.