Scott McDonald fired a double as holders Celtic booked their place in the fourth-round of the Co-operative Insurance Cup in impressive fashion.
Celtic broke the deadlock after 28 minutes when McDonald forced home Paul Caddis's deflected cross.
Falkirk, who had failed to beat Celtic in their previous six meetings, went close through Kjartan Finnbogason.
But McDonald, a solo run and chip by Paddy McCourt and Chris Killen's hooked shot sealed victory for the visitors.
Eddie May's side were seeking their first competitive win since the Europa League win over Vaduz.
But apart from Arfield's 30-yard drive, they failed to test goalkeeper Lukasz Zaluska, who was making his competitive debut for Celtic.
Showing eight changes from the side which beat Hearts, Celtic started strongly.
McCourt and Robson were impressive in midfield for the visitors, with the latter's free-kick clipping the wall before speeding wide.
Robson then fired a shot straight at goalkeeper Robert Olejnik and the visitors went a goal in front just before the half-hour mark.
Killen's clever ball found the rampaging Caddis and his deflected cross broke to McDonald and the Australian striker swept the ball home.
McDonald added his second eight minutes after the break, when Gary Caldwell's header from McCourt's corner fell kindly for the Australian, who turned and sent a shot past Olejnik.
McCourt scored Celtic's third with a superb solo effort, when he picked up the ball on the halfway line and finished his run with a clever chip.
Celtic got their fourth of the night with 17 minutes remaining through Killen after he collected a low cross from Niall McGinn, before Finnbogason's header struck the bar to complete a miserable night for the Bairns.
Aiden McGeady limped off as the visitors played the last 10 minutes with 10 men.
Falkirk manager Eddie May:
Interview: Falkirk manager Eddie May
"We were very poor tonight. Celtic deserved their win and we have to take it on the chin and move on.
"The quality they've got is very good. We created a number of chances, but ultimately we weren't good enough on the night.
"It's up to us get better. We tried to rest a couple of players and Burton O'Brien was a big miss for us in the midfield. But there are no excuses."
Celtic manager Tony Mowbray:
Interview: Celtic manager Tony Mowbray
"We scored some good goals but there's frustration over some of the play.
"We made a lot of changes and it's never going to be ideal. There's some team work that needs to be worked on.
"Any time Pat McCourt steps onto the pitch he can do amazing things. He scored a wonder goal over in Cork recently. It's other areas of his game that he needs to work on.
"He's got to wait for his opportunity. It's always a gamble when you change your team so much. If you lose then you're a lamb to the slaughter, but if I don't play them then I'm never going to know if they can be trusted.
"I need to know these players can come in and do a job."
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