And after Simon Mensing had volleyed them in front Hamilton were the more enterprising side and thoroughly deserved the points.
The victory will go a long way towards ensuring SPL survival for Hamilton but Falkirk are now in a relegation dogfight with Inverness only one point behind them at the bottom.
It was Hamilton who started brightly and Richard Offiong's flick set up Simon Mensing to fire in a 15-yard half-volley that Steven Pressley blocked bravely.
And another fine move from the visitors saw James McCarthy slip Offiong in but this time Darren Barr lunged in with a last-gasp tackle to save the Bairns.
After their whirlwind start Hamilton went behind in bizarre fashion after seven minutes. Neil McCann mis-hit a pass and, without looking up, Chris Swailes turned the ball back towards his own net.
However, Tomas Cerny had moved to the left of his goal anticipating the back-pass and the ball trundled into the empty net to gift Falkirk the softest lead imaginable.
Offiong attempted to rectify the damage with a surging run from halfway but his left-footed shot was always too high.
But Hamilton did get a deserved equaliser after 17 minutes and again a goalkeeping error contributed. Dani Mallo flapped at Brian Easton's corner and only succeeded in knocking the ball to Mensing who crashed home a volley from eight yards to continue his recent goalscoring run.
Falkirk created a clear chance with a fine move. Carl Finnigan skipped away from Easton and his cross was laid off by McCann for Scott Arfield who fired in a low shot that Cerny held low to his left.
But Hamilton, who enjoyed the best of the first-half exchanges, missed an even clearer chance when McCarthy's cut-back was fired wide by the lively Offiong from only six yards out.
This was minutes after Offiong had spun away from Barr and hammered a 25-yard half-volley off the post with Mallo beaten all ends up.
So it was level at the interval despite the visitors' superiority.
Mensing had the first effort of the second half with a 25-yarder that Mallo gathered at the second attempt.
But Falkirk were only inches away from grabbing the lead with a swift break out of defence. Finnigan led the charge and found Steve Lovell with a great ball.
The striker went round Cerny but his shot came back off the post with Mark McLaughlin also colliding with the upright as he attempted to block.
Hamilton hit back and fashioned a great chance for Paul McGowan after good work by Offiong and Mensing but the young striker, on loan from Celtic, blazed his volley yards over the bar.
But McGowan made amends after 76 minutes as he fired Hamilton in front. James McCarthy was the architect with a great ball in behind Barr and McGowan slid in to divert the ball past the advancing Mallo.
And Hamilton could have made sure seconds later when James McArthur fired in a low right-foot shot that took a slight deflection and came crashing back off the post.
Falkirk threw on youngsters Mark Stewart and Kevin Moffat in search of a point and only a great one-handed save from Cerny denied the Bairns as he got down to Patrick Cregg's curling shot.
Hamilton lost McLaughlin, carried off on a stretcher, after a clash of heads with Stewart and the lengthy stoppage contributed to seven extra minutes but Falkirk couldn't find an equaliser.