FALKIRK closed the gap to three points at the top of the table after a smash-and-grab victory, while for Accies it was their sixth defeat in their last eight home games.
The hosts made a positive start and after 17 minutes teenager Andy Ryan got on the end of a Stephen Hendrie cross from the left, but his volley dipped just over.
Seconds later Simon Mensing had a 12-yard shot blocked by goalkeeper Michael McGovern and Ryan, following up, headed over as Accies threatened to dominate. Accies created another opening in 32 minutes when Danny Redmond whipped over a cross from the right which was met perfectly by the head of Martin Canning, but Darren Dods cleared off the line.
Two minutes from the break only a brilliant stop by McGovern from a Mark Stewart snap shot prevented Accies from taking a deserved lead.
Falkirk awoke from their attacking slumbers to stunning effect, Darren Dods heading in a Mark Millar corner from the left from close in, after withstanding a first-half pounding.
Accies substitute Grant Anderson also hit the bar in 76 minutes, just three minutes after coming on, as the woes continued for the hosts.