Lovell: On target for Falkirk
Buoyed by Steve Lovell's second goal in two games moments before half-time, the home side surged further ahead with strikes from Arfield and O'Brien only two minutes apart midway through the second period.
Having given as good as they got for much of the match, Hamilton then capitulated and Arfield netted a fourth from the penalty spot before Robert Olejnik palmed Trent McClenahan's cross into his own net for Hamilton's consolation.
The victory, only Falkirk's second of a difficult start to the season, lifted them off the foot of the table.
It was a poor game of few chances that only came alive after the break.
The visitors' most decisive move in the first-half came after a concerted spell defending their own box.
Whilst Falkirk failed to make real inroads, Accies swept up the field only for Bairns keeper Olejnik to get his full body behind Derek Lyle's left-foot shot.
Falkirk were struggling to get their passing game going, with a lack of movement in front of hesitant defenders seeing moves break down too often in their own half.
The Bairns were also failing to cope with James McCarthy's free role for Hamilton behind lone striker Joel Thomas.
The teenager turned away from home skipper Darren Barr far too easily in the 26th minute and the Scotland defender was lucky that his tug on McCarthy's jersey took place just outside the area and the free-kick came to nothing.
Falkirk finally threatened the Hamilton goal with two chances inside a minute.
First, Graham Barrett swivelled on Michael Higdon's pass but shot too straight at Cerny and then Barrett hit the side netting after Higdon and Lovell had combined to find the Irishman space.
With the break fast approaching, Falkirk finally broke the tedium with a well-worked goal.
Higdon's touch allowed Barrett to scamper into space just inside the box and his cross was knocked in from close range by Lovell.
Hamilton made a tactical switch at the start of the second period, with Mensing being pushed forward from right-back into a central midfield position and Stevenson moving back into defence.
However, McCarthy was again the instigator as Accies almost grabbed the equaliser within a minute of the restart.
The Republic of Ireland under-21 international sent a magnificent reverse pass into the inside-right channel for James McArthur to run on to but the midfielder's shot was too weak and was held by Olejnik.
Both sides were playing better, but the visitors decided on a bold double switch in the 55th minute, replacing Thomas and Lyle with Richard Offiong and Stephen Ettien.
Within three minutes, Ettien came close to an equaliser.
The Frenchman headed David Graham's cross against Olejnik's right-hand post with what looked like the aid of a touch from the Falkirk keeper and the Bairns won the ensuing scramble for the loose ball.
Falkirk midfielder Arfield spoke prior to the game of adding more goals to his game and after a quiet display grabbed a superb second of the season in the 69th minute.
The Scotland under-21 cap ghosted past some despairing lunges as he drove at the Hamilton defence and his left-footed shot beat Cerny low to his left.
Two minutes later, the Bairns sealed all three points with a third.
Cerny was culpable with a poor clearance straight to O'Brien. The summer signing neglected the chance to shoot from distance towards an unguarded net but his eventual drive flew past the keeper for a magnificent strike.
Lovell passed up an excellent opportunity for a fourth in the 79th minute as he blazed just wide from Arfield's pass and Cerny turned aside Higdon's effort eight minutes from time as Falkirk finished on top.
However, John Hughes' side were not to be denied and Arfield swept in a penalty three minutes from time after David Graham had taken down substitute Gerard Aafjes.
The visitors at least grabbed a consolation in the 90th minute as Olejnik could only turn McClenahan's cross into his own net.