After a scrappy opening, international youth striker Paddy Mulvihill poked home past former Bray stopper Matt Gregg, from close range on 12 minutes, in a game that saw Thomas Heary’s debut for the visitors at right-back.
Robbie Doyle scored his second in two games on 32 minutes to bring Bohemians back into the tie – his third of the season, seeing him joint top scorer at the Dublin club with Glen Crowe.
Centre-half Jason McGuinness, a product of the league champions’ schoolboy squad, limped off injured in a second half which saw Crowe sprung from Stephen Kenny’s bench, yet the deadlock failed to be breached.
Extra-time saw the Bohemians' midfield of John Lester and Stephen Caffrey run out of ideas. Sporadic shooting from Longford frustrated the home support and a draw looked likely. But the Bohs' centre-back pairing of Ken Oman and substitute Colin Hawkins stood off sufficiently for Mulvihill to claim his second, with four minutes remaining in extra-time.