A hat trick from Marc Cooper and a brace from Brody Robertson was enough to see off the Poachers.
Cleethorpes Town took an early lead after just four minutes when Marc Cooper lashed home a long cross first time.
The Owls knocked and knocked on the door but Boston's keeper kept the Poachers in the match. However, the Owls extended their lead in the 33rd minute when Cooper once more was on the scoresheet. He latched onto a fine through ball to deftly loft the ball over the advancing keeper to give the Owls a 2-0 lead at the break.
Shortly after the break Cooper completed his hat-trick with a fantastic header from inside the box to all but seal the game for the Owls.
Just five minutes later and it was 4-0. This time it was Brody Robertson who scored. He broke free down the middle and managed to squeeze the ball home.
In the 63rd minute, Peter Winn, the Owls former Scunthorpe United pro broke free but was pulled back and a penalty was awarded. He stepped up himself but his penalty struck the upright much to his dismay.
With just 17 minutes left, the Poachers pulled a goal back through Tony Battersby after Jody Barfords clearance was smashed against the striker who has the easiest of finishes to get a consolation goal.
Brody Robertson, the Owls highest scorer for 2014/15 scored his second goal of the game with 7 minutes left as he latched on a long Daniel Grant pass. He then rounded the keeper and slotted home into the net with ease.
Boston didn't fashion many chances to note in the remaining minutes and whilst the Owls created a few they could not squeeze the ball home.