Celtic will face Kilmarnock in the Scottish Communities League Cup final after overcoming Falkirk at Hampden.
Scott Brown's penalty gave Celtic a 27th-minute advantage.
But Jay Fulton, son of former Celtic and Falkirk midfielder Steve, levelled five minutes before half-time with a composed finish.
Anthony Stokes restored Celtic's lead with an excellent free-kick on 56 minutes and the striker got his second with a tap-in late on.
With the Bairns having knocked Rangers and Dundee United out of the competition in an earlier round, the First Division side were hoping to claim a third Scottish Premier League scalp, while Celtic were looking to continue their push for the domestic treble.
Falkirk's top goalscorer Farid El Alagui was unable to test Celtic goalkeeper Fraser Forster with a first-time shot that flew wide early on.
Celtic began to assert themselves and Brown's well-struck shot was touched onto the post by Michael McGovern.
Gary Hooper converted the rebound only to have his celebrations cut short by the offside flag but television replays suggested the goal should have stood.
The frame of the Falkirk goal was struck again when Thomas Rogne's downward header from James Forrest's corner bounced up onto the bar.
Rogne's presence at a corner was the catalyst for the opening goal as Darren Dods was penalised for grappling with the Celtic defender in the box.
Brown confidently stroked the spot-kick to McGovern's left as the keeper dived in the other direction.
El Alagui's shot into the arms of Forster lacked power as Falkirk tried to respond quickly.
A slack pass from Victor Wanyama allowed the Bairns to mount the attack that would give them their equaliser.
David Weatherston retrieved, pushed down the left and cut the ball inside for Kallum Higginbotham.
Higginbotham had the awareness to spot Fulton's advancing run on the right-hand side of the penalty area and the inch-perfect pass was coolly converted by the 17-year-old.
Rogne was unable to connect with a teasing Brown free-kick and Forrest was denied by McGovern in the closing stages of the first half.
Steven Pressley marched onto the pitch just after the half-time whistle to remonstrate with referee Euan Norris and, as a result, the Falkirk manager watched the second half from the stand.
Fulton scooped the ball over after meeting Higginbotham's high, hanging cross shortly after play resumed.
Rogne was frustrated by the crossbar again with a deflected shot from Charlie Mulgrew's corner and, in the melee that followed, Stokes claimed unsuccessfully for a handball against Murray Wallace before the ball was cleared.
However, Celtic quickly won a free-kick and Stokes superbly curled the ball home to register a goal against his former club.
Fulton's replacement Blair Alston fired wide from the edge of the box before Forster made a double save to deny Dods and Stewart Murdoch as Falkirk continued to threaten.
At the other end, Joe Ledley's effort was deflected wide by Kieran Duffie and McGovern held a curving Mulgrew free-kick.
But Celtic did get a third goal on 86 minutes when Hooper burst towards the bye-line and cut back for Stokes to apply a simple finish.
Neil Lennon's side will return to the national stadium to face Killie on 18 March, .