Falkirk had the ball in the net twice but still left New Douglas Park with a point after a 1-1 draw.
Lyle Taylor knocked the Bairns ahead in the fifth minute when Sean Higgins diverted a Haworth cross into his path at the backpost.
Higgins had the ball in the net too after 24 minutes ramming in Jonny Flynn’s header from close range but he was flagged offside.
Andy Haworth was restored to the Bairns’ line-up and showed some excellent trickery and staked a claim for a regular place with Jay Fulton missing the next eight weeks. Fulton’s central midfield berth was taken by Sibbald while David Weatherston was in an unconventional right-back role, but moved forward in the second half.
By that stage though, Hamilton had levelled. Shortly before half-time Accies strung a series of passes together and in the right-back area and squared to Jon Routledge 20 yards out at the edge of the box. He curled the ball around Michael McGovern and into the corner of the net.
That was it for the scoring though Lyle Taylor slipped through the defence onto a Sean Higgins through-ball and rounded the goalkeeper Kevin Cuthbert. The angle wasn’t impossible but it was tight and the Englishman knocked the ball off the outside of the post.
Andy Haworth also saw a powerful drive parried by Cuthbert and clipped another late chance to the back post which Taylor again just knocked the wrong side of the upright.
However in the last half-hour it was almost all about Accies as they pressed hard for the winner. An excellent save from Michael McGovern was all that stopped Stevie May from handing the home side three points, as the goalie clawed the effort out of the top corner with a reactive stop.
Jon McShane clipped a shot just over the bar after Grant Gillespie had beaten Chris Smith on the left side of the defence and Stephen Kingsley made another brave challenge on the edge of the box to foil McShane – just making contact with the ball in a challenge that could have merited a red card if it was in any way mistimed.