Hibernian finished top of their Scottish League Cup group and progressed to the second round as an unseeded side after beating Peterhead 4-0.
Lewis Miller netted the Hibs opener early on but they had to wait until into the second half for his and the hosts' second, another strike.
David Gray's side began to pull away from their League Two visitors with Rudi Molotnikov converting in the box.
And Nathan Moriah-Welsh's close-range effort put further gloss on the scoreline for Premiership side.
The second-round draw takes place on Sunday and Hibs open their Scottish Premiership campaign away to St Mirren next Sunday (15:00).