Manager Marcus Newell made seven changes to the side which started the FA Vase tie at Billingham, including a completely different back four. Into the side came Laurence McKay, Kieran Wressell, Josh Sunter, Liam Dickens, Jon Oglesby, Marc Cooper and debutant striker Leigh Hutchinson in place of Tim Lowe, Matt Bloomer, Peter Winn, Jack Richardson, Brody Robertson, Andy Taylor and Matty Coleman.
The first half hour was an even affair with few chances at either end. It took a penalty after 31 minutes for the home side to open the scoring as Cooper fired into the right hand corner from the spot after Barton defender Sam O'Malley was adjudged to have handled inside the area.
Dickens almost increased the lead moments later, forcing goalkeeper Rick Watson to dive low to gather his powerfully driven shot. Barton missed a gilt edged chance to equalise on the stroke of half time as Tom Waudby headed wide after finding himself unmarked inside the Cleethorpes penalty area.
An impressive start to the second half saw the Owls quickly wrap up the game, adding two further goals inside the opening 6 minutes. Cooper netted his second of the evening, picking his spot before unleashing a low shot that gave Watson no chance. Hutchinson capped an impressive debut by adding the third less than 4 minutes later, firing sweetly past the despairing dive of the Barton goalie.
The Owls made a number of substitutions, with Andy Taylor adding two more goals within 3 minutes of entering the field. The first was a close range tap in after a neat build up, the second was a well hit shot past Watson after Taylor's initial effort was blocked.
Davis added the sixth goal for Cleethorpes with 20 minutes left to play, tapping home after another well worked build up. The hosts then missed further chances to increase their lead as Oglesby's volley flew just wide before Davis scooped his shot narrowly over the bar.
Barton never gave up and were rewarded for their efforts with a consolation goal in the final minute as James Nichols low shot beat substitute goalkeeper David Birch.
Cleethorpes must wait to find out who their opponents in the final will be with the other semi final between Deeping Rangers and Boston Town still to be played. The final itself will be held at Lincoln City's Sincil Bank stadium, with the date to be confirmed.