The hosts started well - displaying a confidence that has been missing for several weeks - and deservedly took the lead through James McCarthy in a first half they dominated from start to finish.
In the proverbial game of two halves, Falkirk probably edged the second period and sub Michael Higdon equalised with what was almost certainly his first touch.
Hamilton were boosted by the return of influential defender Mark McLaughlin, who had been missing with a medial ligament injury that had kept him out for eight weeks.
Accies nearly opened the scoring after four minutes when Lucas Akins' cross from the right was dummied by Mark Corcoran and McCarthy sent a low shot inches past the post.
Akins forced a save out of Scott Flinders after 13 minutes following some good set-up play by Corcoran and strike partner Richard Offiong.
A powerful run by Brian Easton then created an excellent chance for Akins, but the 19-year-old striker got the ball stuck underfoot and it flew past the right post with Flinders beaten.
But Hamilton made the breakthrough on 36 minutes when Brian Easton's throw-in caused havoc in the Falkirk box.
McLaughlin missed with an ambitious overhead kick and the ball fell to McCarthy, who slammed a right-foot shot high into the net.
Falkirk should have levelled with their first chance of note in 39 minutes, but Darren Barr headed over from a good position yards from goal.
Akins went close from Accies again in 41 minutes, heading an Alex Neil free-kick just over the top right corner.
Falkirk threw on Higdon for Patrick Cregg at half-time and the decision paid dividends almost immediately when Burton O'Brien's cross from the left was flicked on by Stevie Lovell for Higdon to glance a header past keeper Tomas Cerny and into the roof of the net after 49 minutes.
Hamilton nearly regained their lead 10 minutes later, however, when sub Joel Thomas picked out McCarthy, the young midfielder's shot was brilliantly touched over the bar by Flinders.
Gerard Aafjes was unlucky to see his header fly past after 78 minutes having connected with a Neil McCann corner.
Sixty seconds later, Easton's inviting cross was headed inches past by sub David Graham at the other end.
Falkirk had the last chance of note in the 90th minute when Scott Arfield's powerful shot was blocked by Cerny before the Czech keeper gathered.