Carrying a 2-0 deficit into the Easter Road tie, Hamilton fought back to a 2-2 aggregate score when Tony Andreu blasted home in stoppage-time after Jason Scotland had fired them into an early lead.
The Championship side had Hibs pinned back in their defensive third for large periods of the game and their nerve proved stronger than the hosts when it went to spot-kicks.
Hamilton keeper Kevin Cuthbert saved Hibs’ first penalty from Kevin Thomson before diving to his left to deny Jason Cummings and clinch a 4-3 win in the shootout.
There was never any doubt that Hamilton player-manager Alex Neil would make sure a real fist was made after defeat in the first leg at New Douglas Park, but they looked destined to stay in the Championship until Andreu struck right at the death.
Scotland’s 13th-minute strike – a forceful, low shot beneath Ben Williams – grabbed his side a deserved lead but the Hibs keeper produced a string of good saves to keep his side looking likely to survive.
Scott Robinson went close to equalising in the first half and Ziggy Gordon threatened further for Hamilton when he headed over Darian MacKinnon’s cross, before Andreu hit the side netting on the cusp of half-time.
The visitors continued to throw all they had at the Premiership side and substitute Mickael Antoine-Curier almost got onto the end of a superb cross to bag a dramatic second goal and force extra-time.
But that moment of ecstasy fell at the feet of Andreu instead, who volleyed in Scotland’s cut-back with the side of his foot to send the away supporters into pandemonium in the stands.
Chances for both sides were scrappy and half-hearted as they tired in the added 30 minutes. but both Andreu and Hibs’ McGivern had close-range shots blocked inside the area.
And when penalties inevitably came, the momentum stayed with Hamilton as Cuthbert got down low to save from Thomson immediately before Grant Gillespie, Andreu, Antoine-Curier and Scotland dispatched their kicks safely.
Cummings, however, was then in tears, his head buried his shirt, as Hibs followed Hearts out of the top division for the first time since 1999.