Scott Arfield scored twice and Steve Lovell and Burton O'Brien were also on target as Falkirk stretched their unbeaten run to six games.
Accies made five changes from the team that beat Mothewell in extra-time in midweek and looked lively in the early stages.
James McCarthy tried a shot from distance but it was always going wide and Robert Olejnik was not unduly concerned.
A strong run forward from James McArthur stretched the Falkirk defence and Derek Lyle fashioned himself a shooting chance, but it was straight down the throat of Olejnik.
Tomas Cerny put his team in danger when he was indecisive going for a Michael Higdon header with Steve Lovell hovering, but his defence managed to hack the ball clear.
But there was precious little for either set of fans to get excited about around goal.
Arfield swiped a 20-yard shot well wide after Accies had failed to clear an O'Brien free-kick at one end and then Darren Barr blocked a Joel Thomas shot at the other, but it was tepid stuff.
Graham Barrett had a decent chance for Falkirk from a Higdon pass but directed his effort straight at Cerny. The Falkirk striker had another sniff of goal moments later but side-footed his shot into the side-netting.
Barrett then set up Lovell's 44th-minute goal. Higdon set him free on the right with a superb pass and Barrett's cross was touched in at the far post by Lovell.
Hamilton had a chance to get level two minutes into the second half when McCarthy released McArthur with an inspired pass, but the Hamilton midfielder's shot was too close to Olejnik.
Falkirk responded and a terrific shot from Kevin McBride was beaten out spectacularly by Cerny.
Hamilton sent on Stephen Ettien and Richard Offiong after 55 minutes and immediately carried more threat.
Olejnik managed to get his fingertips to an Ettien header to guide the ball onto the post in a frantic goalmouth scramble, but Falkirk then took command with two goals in three minutes.
Simon Mensing gave the ball away in midfield and Arfield took full advantage as he waltzed past defenders before beating Cerny with a crisp finish.
O'Brien did his best to better that when he cracked home an unstoppable left-foot shot from 25 yards after 72 minutes to put Falkirk 3-0 up.
Offiong missed a chance to pull a goal back for Hamilton when he sent an angled shot well over the top with Olejnik out of his goal.
But Lovell missed an even more glaring one after being set up by Arfield when he slid his shot wide from 15 yards with only Cerny to beat.
Arfield made it 4-0 from the penalty spot after Gerard Aafjes had been fouled by David Graham and sub Trent McClenahan scored a late consolation for Hamilton, with a shot that was helped in by Olejnik.