Conor Sammon grabbed the only goal of the first half to hand Killie the lead, before Jamie Hamill saw red for the Ayrshire men.
Antoine-Curier then came off the bench to earn a point but it was not enough for relegation contenders Hamilton to draw level with nearest rivals Hibernian.
Hamilton handed a debut to Aaron Wildig, who was given the nod after signing on loan from Cardiff, while Simon Mensing was suspended.
Kilmarnock were without Alexei Eremenko, who was also banned, but new recruit Willy Aubameyang was named on the bench following his move from AC Milan.
Killie had the best of the chances early on and could have taken the lead when a long ball from Hamill was collected by Tim Clancy out on the right flank.
He raced into the box and tried to cut back for Sammon who was loitering in front of goal but goalkeeper Tomas Cerny did well to intercept before the striker could make contact.
Clancy then saw his header flash just wide of the post from close range from Garry Hay's corner as the visitors continued to press for the opener.
Their hard work paid off when they surged into the lead with 15 minutes gone. Mehdi Taouil provided the pass and Sammon was able to shrug off Mark McLaughlin before rifling past Cerny.
Kilmarnock were dealt a blow when Hamill was dismissed after 29 minutes after picking up a second yellow card for a second challenge on Flavio Paixao.
Both sides quickly made changes, with Accies swapping Nigel Hasselbaink and Gavin Skelton for Antoine-Curier and Damian Casalinuovo, while Rui Miguel was withdrawn for Killie and replaced by new signing Aubameyang.
Casalinuovo had the ball in the back of the net within a few minutes but the offside flag denied Hamilton the equaliser.
Hamilton emerged for the second half determined to haul themselves back into the game and had a couple of half chances in front of goal.
But only the efforts of Cerny prevented them from falling further behind when the goalkeeper produced an excellent block to prevent the impressive Taouil's angled drive from hitting the back of the net.
Accies were then forced to use their final substitution when McLaughlin injured himself after falling over the advertising hoardings and was replaced by Grant Gillespie before being strapped to a stretcher following several minutes of treatment.
A cross-shot from Dougie Imrie sneaked into the bottom corner as the home side pushed for a leveller but the assistant referee flagged before the effort had even crossed the line.
Hopes of an Accies comeback could have been dashed when Sammon whipped into the path of Liam Kelly and he looked certain to leave the net bulging only to hook over the crossbar instead.
Sammon also turned provider for Taouil with a neat-cut-back but he was also off-target with a poor shot that fell wide of the upright.
Instead, it was Hamilton who were on target with 11 minutes to go when Antoine-Curier collected on the corner of the area and lashed an unstoppable shot past the helpless Cammy Bell.