A misjudgment from goalkeeper Kevin Cuthbert handed Falkirk the lead as he reacted too late to Jay Fulton's free-kick which drifted in at his near-post shortly after 50 minutes.
Cuthbert made amends by denying Fulton a second goal and it proved a pivotal point in the game.
Mickael Antoine-Curier equalised in the 70th minute when he outsprinted the home defence to shoot low past Michael McGovern and three minutes later, Ali Crawford curled the ball home from 20 yards for the winning goal.
Alex Neil, Hamilton's player-manager, believed it was an important result but warned that there is a downside to Hamilton's 100 per cent start to their league campaign.
"The only problem we have now is expectation levels from everybody," he said. "They are going to expect us to go here, there and everywhere and pick up points and win games and that isn't going to be the case here.
"This is a tough league with some very good sides."
Cowdenbeath gathered their first points of the season and did so in dramatic fashion with Kane Hemmings scoring a last-minute winner in a 3-2 victory at home to Dumbarton.
Shortly before the winning goal, Jamie Ewings had kept out a Jordan Morton penalty and looked to have earned a point for Dumbarton. But Hemmings, who had looked dangerous all afternoon, settled matters.
Cowdenbeath dominated the first half but all they had to show for their efforts was a goal from Jamie Stevenson midway through the half.
Chris Turner equalised six minutes into the second half when Cowdenbeath goalkeeper Grant Adam was caught out by his shot from outside the penalty area. Turner then scored his second with a crisp, 20-yard strike which left Adam with no chance.
But Jon Robertson, who re-signed for the Fife outfit earlier in the week, levelled on 72 minutes after poor Dumbarton defending. Hemmings then contributed the winning goal after Ewings' heroics.
Morton and Raith Rovers shared a 1-1 draw at Cappielow with Grant Anderson earning the Fife side a point with a 78th-minute header.
Morton had the better of the first half but found David McGurn in fine form in the Raith goal. He pushed away an early shot from Tony Wallace and was only beaten by Dougie Imrie's emphatic penalty late in the first half.
Raith, who had hit the crossbar through Kevin Moon in the first half, pressed in the second half and midfielder Anderson beat Nicolas Caraux with a well-placed header from Lewis Vaughan's cross with 12 minutes left.
Queen of the South and Alloa Athletic drew 0-0 at Palmerston Park in a match where neither side deserved to take full points.
Alloa had their chances - Andy Kirk failing to get any power on an early header and then being denied by Callum Antell late in the first half.
Derek Lyle had a couple of opportunities for Queen of the South in the second half but could not cash in as the game ended in stalemate.