The on-loan Colchester striker curled home from 25 yards and then coolly rounded Graham Stack as Accies moved above Aberdeen in the Scottish Premier League.
Simon Mensing had earlier twice given Hamilton the lead with superbly-taken penalties as Hibs suffered a serious blow to their Europa League aspirations despite enjoying dominant spells either side of Colin Nish's equaliser.
The visitors have now won just twice in 13 matches and their misery was completed when Tomas Cerny celebrated his 25th birthday by saving a penalty from Hibs substitute Abdessalam Benjelloun.
The damage had been done by then as Thomas, whose previous 36 appearances for Accies had yielded just one Co-operative Insurance Cup goal, showed why Billy Reid brought him back to New Douglas Park in January.
Hamilton, who had gone six matches unbeaten before their narrow defeat at Ibrox last weekend, brought back James Wesolowski from suspension with Grant Evans coming in and David Elebert and Brian Easton absent.
The hosts started well and Stack had to scramble to push away Mickael Antoine-Curier's flick following James McArthur's cross.
Hibs soon created their first chance when they worked the ball to Anthony Stokes but his powerful strike from 16 yards was pushed wide by Cerny.
Flavio Paixao shot over from a tight angle before earning Hamilton their first penalty. Mensing released Paixao on the left edge of the box with Hibs stretched and the covering Liam Miller blocked the resulting shot with his hand.
Steve Conroy pointed to the spot but took no further action, however the referee intervened after Mensing converted the penalty, ordering a retake after two Hamilton players encroached. Mensing dispatched his second effort into the same top corner to give Accies a 16th-minute lead.
Stokes then diverted John Rankin's free-kick over and Hibs stepped up the pressure.
Cerny had a fortunate escape when he was beaten to Derek Riordan's corner by Sol Bamba, but the ball ricocheted off Ian Murray and into the goalkeeper's hands.
The visitors were soon level in the 33rd minute though when Nish nodded home at the back post after Darren McCormack's deflected cross.
Hibs finished the half on top and Cerny spilled Rankin's low drive, but the Czech recovered just in time to hold before Nish followed in.
The visitors resumed where they left off at the start of the second period and Martin Canning threw himself in front of Rankin's volley to divert it over before Riordan sliced well wide after Nish's lofted ball.
But Hamilton soon benefited from their second penalty on the hour mark.
Canning's free-kick found Dougie Imrie and he got round the outside of Murray before being hauled down as he ran along the byline. Canning and Thomas, who had just replaced Antoine-Curier, became involved in a shoving contest as the sub looked to take the spot-kick.
But Mensing again retained his composure after a delay as Kevin McBride replaced the injured Miller, and found the top corner with an identical finish.
Stack soon blocked a one-on-one from Wesolowski and pushed over Imrie's deflected cross but there was nothing he could do about Thomas' 68th-minute strike.
There appeared to be little danger when the forward took possession of the ball near the left touchline but he worked space for a glorious 25-yard shot into the far top corner.
Hamilton continued to threaten and Stack held Mark McLaughlin's shot after a half-cleared corner and twice made brilliant stops from Paixao.
Nish missed the target from eight yards after Steven Thicot's blocked shot fell into his path and Hibernian's chances evaporated in the 80th minute.
Thomas pounced on a loose ball just outside the box and brushed off last defender Bamba before rounding Stack and slotting home.
The visitors soon won a penalty when Canning tripped Rankin but Benjelloun's weak effort was blocked by the legs of Cerny.