Falkirk followed last week's Ramsdens Cup win over Clyde with a Scottish League Cup victory against the same opposition.
Blair Alston fired in from close range to give the Bairns the lead as the match neared its final quarter-hour.
A fine strike from the edge of the area by Philip Roberts doubled Falkirk's lead.
And Thomas Grant's emphatic finish rounded off a comfortable win for the hosts.
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