Two goals from Blair Alston gave the Accies the advantage but they had to survive a nervous end to the contest after substitute Andy Ryan pulled a goal back 16 minutes from time.
The first decent opportunity of the game fell to Hamilton's Jon Routledge but he shot just wide after Gary Fisher had played him in.
Fisher then had a chance to score himself after outwitting a slumbering Falkirk defence but his effort lacked power and the chance went begging.
The visitors battled back and almost took the lead through Alston after he intercepted a loose pass from Routledge only for Accies goalkeeper Kevin Cuthbert to make a comfortable save.
Cuthbert was then called upon to pull off a stunning stop to keep out striker David Weatherston's drive as the tempo of the game increased.
Fisher then went close at the other end with a shot that fizzed just wide of the mark before the defender played in Louis Longridge, who drilled his effort beyond the post.
Hamilton were then made to pay for their profligacy in front of goal a minute before the break as Alston nipped in to score from close range.
Falkirk almost doubled their lead after the restart, Lyle Taylor's shot coming back off the crossbar, with Sean Higgins doing well to deny Cuthbert as he reached the rebound first.
The home side rallied though and Michael Devlin headed over before Alston pounced again in spectacular fashion to grab his second goal of the contest.
Hamilton failed to clear a Weatherston corner and Alston volleyed into the top corner from 25 yards (71).
Again Billy Reid's rallied and they pulled a goal back just three minutes later through Ryan, who slotted home after keeper Michael McGovern could only parry Fisher's shot into his path.
Ryan should have equalised but he somehow guided the ball over from just two yards after Stevie May had played him in.
Jonathan Page also went close with a header that missed the mark and the same player was sent off late on for a high two-footed challenge on Taylor.