Chris Mitchell broke the deadlock with a stunning free-kick in the 64th minute and Lee Bullen blasted home the second 11 minutes from time after coming on as substitute.
Falkirk got their reward for a more direct second-half approach after being put under pressure for long spells during the opening period.
The pitch at the Falkirk Stadium put up a strong resistance to the driving rain that preceded kick-off and the Bairns created the first chance after just two minutes.
Ryan Flynn's ambitious 40-yard shot was clutched by the back-tracking Tomas Cerny who had moved from his line.
Flynn was teed up in the middle of the park after fans' favourite Pedro Moutinho showed great skill to create the space.
At the other end moments later, Mickael Antoine-Curier should have done better after Mitchell's clearance was deflected into the on-loan Dundee striker's path but goalkeeper Robert Olejnik darted from his goal to steal the ball at the marksman's feet.
Accies midfielder James Wesolowski was then afforded space on the edge of the area but his low shot drifted past the post.
Hamilton made the more dominant start of the two sides although Falkirk fashioned another chance in the 19th minute when Vitor Lima drilled a low effort that Cerny got down to.
Textbook defending by Bairns centre-half Brian McLean ensured Antoine-Curier's shot from just inside the box was blocked after the marksman latched on to Richard Hastings' long ball.
The home supporters became restless over their side's lack of cohesion on the pitch although they appreciated Flynn's shot that was deflected just wide of the far post.
From the resulting corner, Mitchell's delivery caused Accies all sorts of problems as Danijel Marceta's effort was blocked before the danger was eventually cleared.
Falkirk breathed a sigh of relief three minutes before the break as Antoine-Curier mis-hit a tame shot at Olejnik after being set free by James McArthur's superb left-footed diagonal pass.
The hosts emerged for the second half with more purpose about their play as they had their visitors pegged back for spells following the interval.
Carl Finnigan showed great skill to edge past Hastings on the wing but his driven cross was cleared.
Mitchell eventually gave Falkirk the lead in the 64th minute when he floated a superb 25-yard free-kick over the wall and into the top corner of the net from an angle.
The set-piece was awarded after Moutinho was felled as he made for goal.
Moments later, Falkirk had Olejnik to thank for ensuring their advantage remained as he produced a fine close-range save to deny Simon Mensing, who had latched on Marco Paixao's cut-back.
The Austrian shot-stopper then turned Wesolowski's stinging long-range effort behind.
With Eddie May's first win as manager and Falkirk's maiden victory in the league within touching distance, it was not surprising when the Bairns manager gave the more defence-minded Pele his debut in place of Flynn.
May also brought on veteran Bullen to replace the tiring Moutinho, who is still short of match fitness.
And the former Dunfermline and Sheffield Wednesday utility player doubled his side's advantage in the 79th minute.
With Accies reverting to a three in defence, Finnigan played through Bullen and he blasted the ball high into the net from close range.
Scott Arfield came close to making if three with an audacious flick inside the six-yard box that was saved by Cerny.
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