Match ends, Celtic 3, Falkirk 0.
James Forrest scored on his first Celtic start since September as the Scottish Cup holders overcame Falkirk's stubborn resistance in the third round.
The winger found the net with the aid of a deflection after the League 1 leaders had kept their hosts at bay for 55 minutes.
Ryan Christie's low strike quickly doubled the lead.
And substitute Mohamed Elyounoussi's deft chip gave Celtic a scoreline that better reflected their dominance.
With Eddie Howe in advanced talks to become Celtic's new manager, victory maintains their hopes of a record-extending fifth successive Scottish Cup.
David Turnbull's low bending shot was pushed wide by Robbie Mutch in the opening minutes and Leigh Griffiths turned wide at the resulting corner when he really should have scored.
Christie also threatened but his three first-half efforts were all too high, as was a Turnbull free-kick.
Kristoffer Ajer's marauding runs became a feature of the match and the Norway defender fired wide at the end of one venture into Falkirk territory.
Griffiths, who had a first-half penalty appeal turned down, tested Mutch early in the second period as the hosts' relentless pressure continued.
And when the opener came, it had a touch of fortune as Forrest retrieved Tom Rogic's pass on the left of the Falkirk box and fired into the opposite corner off Lewis Neilson's head. It was the Scotland player's first goal since an ankle injury in September kept him out for almost six months.
Falkirk had struggled to retain possession whenever they got beyond their own defensive third and their task grew much harder when Christie turned on the edge of the box and beat Mutch at his near post.
Mutch continued to be busy with another Turnbull effort blocked. Forrest hit the rebound narrowly wide and soon made way for Elyounoussi, having previously made just two substitute appearances in 2021.
And Elyounoussi made an impact off the bench, latching on to Jonjoe Kenny's cross and flicking the ball over Mutch.
Kenny and Griffiths' replacement Albian Ajeti missed further Celtic chances before captain Scott Brown, who will join Aberdeen this summer, forced a late save by Mutch.
What did they say?
Celic winger James Forrest: "I'm delighted. Starting was a big achievement. It's great to add the goal. The first couple of months was definitely the hardest. Since the turn of the year I've been back in amongst the team training. I just want to keep doing what I'm doing just now."
Celtic interim manager John Kennedy: "We've missed James Forrest. He's an eliminator, he's direct and he's hungry for goals. It's great to have him back and good to get him on the scoresheet.
"Second half, the boys were terrific - very professional, kept the ball moving, tired Falkirk out and then the spaces open up. The guys we've got in the team, they've got massive quality and that comes through in the end."
Falkirk co-manager Lee Miller: "It was always going to be a tough ask for us to compete with them for 90 minutes. Really proud of the way the boys applied themselves. I thought we defended really well.
"The fighting spirit was there for all to see. It's a great experience for them. Everybody worked hard right until the final whistle. We're not going to be judged on this, our bread and butter is the league."
- 49ForrestSubstituted forElyounoussiat 74'minutes
- 18RogicSubstituted forSoroat 72'minutes
- 9GriffithsSubstituted forAjetiat 62'minutes
- 24FotheringhamSubstituted forTelferat 64'minutes
- 17LeitchSubstituted forAlstonat 64'minutes
- 10DowdsSubstituted forKeenaat 51'minutes
- John Beaton
- Shots on Target
Second Half ends, Celtic 3, Falkirk 0.
Offside, Celtic. David Turnbull tries a through ball, but Mohamed Elyounoussi is caught offside.
Foul by Ryan Christie (Celtic).
Charlie Telfer (Falkirk) wins a free kick in the defensive half.
Attempt saved. Scott Brown (Celtic) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Ryan Christie.
Attempt missed. David Turnbull (Celtic) right footed shot from the centre of the box is close, but misses to the right.
Attempt missed. Albian Ajeti (Celtic) left footed shot from the centre of the box is close, but misses to the right. Assisted by David Turnbull.
Attempt blocked. David Turnbull (Celtic) right footed shot from the left side of the box is blocked. Assisted by Albian Ajeti.
Foul by Albian Ajeti (Celtic).
Scott Mercer (Falkirk) wins a free kick in the defensive half.
Attempt blocked. Jonjoe Kenny (Celtic) right footed shot from the right side of the box is blocked. Assisted by Mohamed Elyounoussi with a cross.
Goal! Celtic 3, Falkirk 0. Mohamed Elyounoussi (Celtic) right footed shot from the centre of the box to the centre of the goal. Assisted by Jonjoe Kenny with a cross.
Attempt missed. Mohamed Elyounoussi (Celtic) right footed shot from outside the box is close, but misses the top right corner. Assisted by Diego Laxalt.
Substitution, Celtic. Mohamed Elyounoussi replaces James Forrest.
Substitution, Celtic. Ismaila Soro replaces Tomas Rogic.
Attempt blocked. James Forrest (Celtic) right footed shot from the centre of the box is blocked. Assisted by Tomas Rogic.
Attempt missed. Ryan Christie (Celtic) left footed shot from the right side of the box misses to the left. Assisted by Tomas Rogic.
Foul by Diego Laxalt (Celtic).
Akeel Francis (Falkirk) wins a free kick on the right wing.