Scorers: Falkirk - Beck (80); Hamilton - MacKinnon (60)
Darian MacKinnon broke the deadlock for the visitors on the hour, finally finding the net following a series of missed chances, particularly in the opening period.
However, the Bairns belied the fact they were playing their third match in seven days to equalise from close range through Beck, who had earlier struck the bar, following a stunning assist by Rory Loy.
Just one point separated these sides in the final Championship standings, and it would take a brave man to pick a winner for the second leg on Sunday.
Indeed, the only thing that seems certain after this enthralling affair is that you would fancy either side to provide a serious threat to Hibernian’s Premiership status.
Falkirk’s extra-time win over Queen of the South on Saturday was described by goalkeeper Michael McGovern as being akin to two exhausted heavyweight boxers desperately knocking lumps out of each other, such was the monumental effort and evident fatigue.
And whether attributable to fatigue, sloppiness or the absence of the immensely stabilising figure of David McCracken in defence, Falkirk started in woeful fashion against the well-rested Accies.
It took just five minutes for Jason Scotland to get a clear sight on goal, taking advantage of some calamitous defending in which Will Vaulks and Johnny Flynn crashed into each other, opening a clear passage to goal. However, McGovern spread himself to make a superb point-blank stop.
Minutes later it was Scotland versus McGovern again. This time the bustling striker got the better of the Falkirk goalkeeper by skipping around him with aplomb – only to see his attempt to roll the ball into an empty net thwarted by Flynn.
Hamilton were flying. So much so that the light-hearted chants of “we want ten” suddenly only seemed partly ironic. Indeed, with just ten minutes on the clock, McGovern was forced into another important save, this time blocking an Ali Crawford drive at the front post after some neat work from Anthony Andreu.
It was Andreu’s turn to have a pop at McGovern next, with the gifted playmaker exchanging slick passes with Scotland before dashing through on goal. However, he pulled his shot wide of the post from a prohibitive angle. Under siege for so much of the half, Falkirk rallied admirably towards the break, with a sharp Beck drive from inside the box forcing a low save from Kevin Cuthbert.
While their own goal continued to lead a charmed life – Millar denying Accies a certain opener by clearing a Martin Canning header off the line – Falkirk had the best chance to go in ahead at the interval.
Beck utilised his substantial six-foot-seven frame to flick a Loy cross towards goal. The clever effort looked for all the world to be looping into the net, only for Cuthbert to produce a marvellous one-handed save, parrying on to the crossbar.
Falkirk continued to press after the break and were again left cursing the brilliance of Cuthbert. This time it was Rory Loy who saw a fantastic low drive from the edge of the box parried wide by the former St Johnstone goalkeeper. It was becoming inexplicable that this match had not heralded a goal. MacKinnon remedied that on the hour-mark. The combative midfielder picked up a Crawford pass at the angle of the box and, with Vaulks standing off him, took the invitation to curl home a superb curling opener. You could forgive Falkirk for wilting given their recent exertions.
Yet nothing could have been further from the truth and, with ten minutes to play, Loy dashed down the left flank and produced a stunning low delivery across the face of goal for Beck to tap home.
This thoroughly enthralling encounter still had time for McGovern to pull off another two splendid saves. The Northern Ireland international stooped low to block a Louis Longridge shot from eight yards before holding on to a point-blank Mickael Antoine-Curier header
Falkirk: McGovern; Vaulks, Flynn, Kingsley, Dick; Alston, Millar, McGrandles, Sibbald (Shepherd 72), Loy, Beck. Subs not used: Bowman, Durojaiye, Leahy, Rowan, Blair, Biabi.
Hamilton: Cuthbert; Gillespie (Kilday 82), Canning, Tena, Gordon; MacKinnon, Routledge; Crawford (Ryan 87), Andreu, Longridge; Scotland (Antoine-Curier 63). Subs not used: Currie, Devlin, George, Keatings.