Falkirk went on the offensive at the start of the second half with Murray Wallace being denied by Hutton from close range. Millar rifled in two shots in quick succession from 25 yards out and again Hutton stood firm, but his evening changed when he was judged to have pulled the legs from under David Weatherston.
After he had been dismissed, Millar drove the spot-kick past youngster Blair Currie and, as Hamilton looked to settle, Farid El Alagui carved open their defence and Millar side-footed home from 16 yards out, before Duffie skipped down the right and sent over the perfect cross for El Alagui to nod home a third.
Falkirk: McGovern, Duffie, Dods, Wallace, Scobbie, Sibbald, Fulton, Millar, Gibson, El Alagui, Weatherston. Subs: Bowman, Bennett, Kingsley, Faulds, White.
Hamilton: Hutton, McAlister, Canning, McLaughlin, Hendrie, Redmond, Mensing, Neil, Routledge, Ryan, McShane. Subs: Currie, Kilday, Gillespie, Stewart, Spence.
Referee: C Allan.