Two goals from Tom Taiwo was enough to defeat Dunfermline on Tuesday night.
And the second half performance pleased Falkirk boss Peter Houston, though the actions of Botti Biabi did not.
The forward was red-carded just 20 minutes after entering the field as a second-half substitute.
He did however set-up both Taiwo’s strikes which put the Bairns into the quarter-final draw at Queen’s Park on Thursday.
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