The rock-bottom Accies opened the scoring through Simon Mensing and had looked set to hold on for a famous win until the final minute of a dramatic encounter at New Douglas Park.
James Forrest and Jim McAlister were both sent off earlier in the game and Mensing joined them when he conceded the last-gasp spot-kick which was converted by Anthony Stokes.
Freddie Ljungberg was dropped to the bench as Celtic made three changes from the Scottish Cup win over Berwick Rangers, Georgios Samaras missing out through injury and Fraser Forstergiven the nod in goal ahead of Lukasz Zaluska.
Hamilton made one change from their win over Alloa, with Marco Paixao making way for Gavin Skelton, while new signing Mickael Antoine-Curier was named among the substitutes.
Celtic had the chance to pile on the pressure when they won a free-kick on the left flank and Charlie Mulgrew whipped a dangerous ball into the box for Paddy McCourt in front of goal, but Mark McLaughlin was first to the ball to nod into the hands of goalkeeper Tomas Cerny.
At the other end, Mensing tried to open the scoring for Hamilton but his shot from just inside the box was tame and it was comfortably gathered by Forster.
The breakthrough came after 28 minutes, and surprisingly it went Hamilton's way. Flavio Paixao lofted the ball into the box and although Forster managed to block, Mensing pounced to nod home. Martin Canning appeared to be in an offside position in front of the goalkeeper but the goal was allowed to stand.
Celtic tried to haul themselves back into the game and could have levelled when Cerny's attempts to clear a Mulgrew cross fell at the feet of Forrest 15 yards out but he blasted well over the crossbar.
With half-time approaching, irate Celtic boss Neil Lennon - who found himself in the spotlight after picking up a six-match touchline ban starting next week - earned himself a lecture from referee Willie Collum.
Celtic suffered another setback just four minutes after the restart when Forrest dived in late with a rash challenge on David Buchanan and was shown a straight red card, with the Accies player requiring treatment before being able to continue.
With just under an hour gone, Celtic made their first change when Beram Kayal was withdrawn to allow for the introduction of skipper Scott Brown, who came off the bench to score at Berwick at the weekend.
Accies threw McAlister into the action in place of McLaughlin after 62 minutes but he was sent off after just 35 seconds on the field following a reckless tackle on Mark Wilson, who was replaced by Niall McGinn moments later.
Now that the number of players on each team was level again, Celtic set about trying to level the scoreline too and Stokes saw his ferocious drive from 25 yards gratefully smothered by Cerny.
With time fast running out for the Hoops, Joe Ledley was withdrawn for Ljungberg, as the former Arsenal star was given his first taste of the SPL.
Cerny was called into action again when Dougie Imrie's clearance smacked off Stokes and rebounded towards goal. Daniel Majstorovic - who netted his first goal for Celtic at the weekend - then nodded wide from the corner.
Just when Accies thought they had held on for the win, the referee pointed to the penalty spot in the last minute, as Mensing was sent off for a foul on Emilio Izaguirre in the box. Stokes stepped up to send the goalkeeper the wrong way with the spot-kick.
Stokes then thought he had grabbed the winner at the death but Izaguirre's corner had gone out of play before he forced home a header as the match ended all square.