Scott Brown’s penalty gave Celtic a 27th-minute advantage only to see Jay Fulton, son of former Celtic and Falkirk midfielder Steve, level matters 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.
And they were not to be denied today.
Speaking after the game Neil Lennon has confirmed Celtic’s transfer coup over Old Firm rivals Rangers with the signing of Ibrox target Pawel Brozek from Trabzonspor.
Rangers manager Ally McCoist confirmed his interest in the Polish striker over the weekend but the Parkhead club have agreed terms with the player and subject to a medical he will sign on loan until the end of the season, with a permanent deal on the table.
The Celtic boss was speaking at Hampden after Anthony Stokes scored twice in the Hoops’ 3-1 Scottish Communities League Cup semi-final win over Falkirk to set up a final meeting with Kilmarnock.
“I know Rangers were interested but we have been involved with players before and Rangers have nipped in,” said Lennon.
“I am not saying we have nipped in, but we have been tracking him for quite a while. We have tried to keep it under the radar.
“I have not seen him yet but if he does come in I will be delighted.
“We will see how he is and if he is ready to go he won’t be far away from starting. He scored a lot of goals in Poland and he will give the squad a jag.
“We can’t keep relying on Gary Hooper and Stokesy for the goals.
“If one of them gets injured or suspended we could be a goalscorer short and Pawel is a goalscorer.
“He has gone to Trabzonspor and for one reason or another it has not worked out but what we do know is he is a goalscorer.
“He is a bit like Hooper, he knows where the goal is. We might try to get another player in before the window closes, we are always looking.”