St Mirren are now in the drop-zone and with the Bairns meeting Saints at the Falkirk Stadium on Saturday, relegation is probably now between those two clubs.
But although they can breathe more easily than most, Hamilton are still involved in the dogfight and now must take at least a point from their clash against Motherwell on Saturday to guarantee their safety.
Over the piece Falkirk's win was just about deserved and they probably needed it more than their hosts.
However, the margin of success is slender; a win would have secured Accies' top-flight status, while defeat drags them into battle again.
It was obvious from the start that this was going to be a tense encounter, but Hamilton had the better of the first half and should have made more of their chances.
In 16 minutes James McCarthy and Brian Easton combined down the left, with the latter cutting the ball back superbly for Paul McGowan, who seemed to freeze and the ball got away from him.
Five minutes later a great move was ended when Mark McLaughlin headed the ball down for Martin Canning, whose fierce shot was well blocked. The ball fell to Easton, but his sizzling 19-yard drive was brilliantly tipped over by Dani Mallo.
Falkirk stopper Steven Pressley was fortunate to stay on the park in 37 minutes when he cynically took McCarthy out of the game just over the halfway line and with no attempt to play the ball, but referee Mike McCurry saw fit only to caution the former Celtic star.
The Bairns almost took a lead into half-time when Carl Finnigan's cross from the right was headed across goal and past the right post by Michael Higdon.
But Falkirk scored the winner in 60 minutes when Neil McCann played Steve Lovell through and although Tomas Cerny blocked his shot, the ball fell to Scott Arfield, who clipped a delicate shot in via the left post.
Hamilton nearly levelled just four minutes later. Sub Joel Thomas picked out McCarthy, his shot was blocked but fell into the path of James Gibson and as he prepared to shoot, the ball was desperately hacked clear.
Fifteen minutes from time Easton's cross from the left was cleared only as far as McCarthy and his angled shot crashed off the crossbar and over.
In 87 minutes Easton's cross from the left was flicked on by Thomas but sub Kenny Deuchar headed just past the right post.
In the final minute of normal time sub Stuart Taylor knocked the ball down to McCarthy, but his shot was deflected past.
The midfielder still had drive to try and grab an equaliser, but sent a diving header just over two minutes into stoppage time.