In front of a bumper 4,210 crowd, the game started slowly, with Hearts backing off the first division champions in the early stages.
However, Hearts soon got into their stride and took the lead on 18 minutes when Andy Driver's corner from the right was headed in by Marius Zaliukas, despite Tomas Cerny's efforts to keep it out at the back post.
Accies were dealt a further blow when Chris Swailes limped off seconds later, to be replaced by James McCarthy.
The young midfielder nearly got on the scoresheet just three minutes later when he latched on to a superb diagonal ball by Richard Offiong, but keeper Marian Kello blocked well with his chest.
Hearts should have scored in 37 minutes when Laryea Kingston mugged Brian Easton on the right and played in Eggert Jonsson, but he sliced his shot well wide.
Simon Mensing was unlucky to see his 25-yard effort fly inches wide of the right post in 41 minutes.
Cerny then produced a simply breath-taking save to claw David Obua's deft head-flick out of the bottom left corner, following good set-up play by Michael Stewart on 44 minutes.
Hamilton came out in the second half and flew at Hearts, but failed to sufficiently hurt the visitors.
David Elebert sent a wicked cross over the face of goal in 47 minutes, and three minutes later McCarthy's cross was headed over by striker Lucas Akins.
But Hearts doubled their lead in 59 minutes when Mensing lost possession to Driver and the midfielder drove through on the left, evaded Mensing's desperate challenge and drilled low into the right corner.
That seemed to knock the stuffing out of Accies, but they eventually hit back in 80 minutes when Elebert's cross from the left was headed past Kello by sub Derek Lyle.
With five minutes remaining Kingston had a free-kick blocked, but collected the rebound and burst into the box, only to send his angled shot inches past the right post with Cerny beaten.