Grayson named four changes to his side as Preston lined up in a 4-4-2 formation. Clarke partnered Huntington at the back with Keane reverting to right back and Laird on the opposite flank.
Brownhill paired with Welsh in midfield whilst Holmes roamed from wing to wing with Gallagher. Beavon and Garner started up front as the front four effectively interchanged.
Preston started off pressing well but the game changed when Barnet were reduced to ten men with Marsh-Brown seeing red for a challenge on Laird less than a quarter of an hour in.
The visitors could not cope as Preston took control. The home side were soon in front and never looked back as Tom Clarke notched another header from a cross.
The lead was then extended before the break when Garner headed home from close range unmarked and Gallagher scored his first for the club just before half time.
Holmes hit the bar from a free kick in the second half before Preston were reduced to ten men after Beavon was sent off for a sliding challenge. He now misses the next three games.
Preston were not deterred and Gallagher managed to score two close range efforts to secure a hat trick and the matchball. The first by a loan player at Preston. Garner added the final goal late on when put clean through.
North End will face either Wycombe or Crewe in the next round.