The League 1 champions were kept at bay for 44 minutes of the first half before Michael Moffat, the beneficiary of an error by visiting goalkeeper Robbie Mutch, broke the deadlock.
Dunfermline picked up the pace after the break and Arbroath failed to cope. Andy Geggan added a second before Moffat struck again.
The Pars fans also got to see new signing Kallum Higginbotham in action after the former Partick and Kilmarnock playmaker was introduced in the second half.
The Fife outfit’s next Group C assignment is at neighbours Cowdenbeath on Saturday, while Arbroath have the weekend off.
Dunfermline boss Allan Johnston resisted the temptation to make wholesale summer changes following their promotion from League 1. The Pars lined up with only three new recruits: Lee Ashcroft, Nate Wedderburn and Gavin Reilly, and they made a dominant start.
Rhys McCabe sliced a left-foot shot wide from the edge of the box after taking in Joe Cardle’s pass before a flowing move involving Wedderburn and Geggan led to Moffat having a 15-yard drive which was pushed behind by Mutch.
Arbroath, who held Dundee United to a draw over 90 minutes in Friday’s Group C curtain raiser, conjured up their first opportunity after 26 minutes but Pars keeper David Hutton got down well to an opportunist prod inside the box by Ryan McCord.
After riding their luck for much of the half, the manner in which the visitors conceded the breakthrough goal a minute before the break would have been of huge frustration to the part-timers.
Arbroath’s 17-year-old goalkeeper Mutch, who is on loan from Aberdeen, ill-advisedly rushed outside his box in a bid to make an interception. But Reilly got there first and his cross was placed into the unguarded net by Moffat.
Mutch partially atoned for his error after the break with a good save to deny Moffat before the goalscorer swept a Reilly cross over the bar.
In between those Moffat chances, Arbroath’s Omar Kader had an effort saved before Bobby Linn’s curling shot was pushed away at full-stretch by Hutton.
But after Cardle cracked a drive off the post, Dunfermline strengthened their lead in the 62nd minute when Reilly’s cross was cushioned into the path of Geggan who poked the ball through the legs of Mutch.
Moffat made sure the result was beyond doubt in the 66th minute when he directed Ryan Williamson’s low cross into the net from close range.
Arbroath finished the game with ten men after Ricky Little was shown a straight red card for a crunching tackle on Paul McMullan.