Sedge got off to a flying start in their match against North West Counties Premier side Barnoldswick, breaking the deadlock through debutant Lewis Whitham with only three minutes gone.
It was 2-0 just 11 minutes later when Gav Allott pounced from close range and the win was wrapped up on 53 minutes thanks to Spencer Harris' long-range strike.
The quarter-final date is to be confirmed.