Liversedge produced a determined display but found Cleethorpes goalkeeper Damien Steer in inspired form last Saturday.
Steer thwarted Sedge on numerous occasions and helped his side record a 3-1 victory, which moves them up to third place in the Northern Counties East League Premier Division.
Things did not start well for the visitors as Brody Robertson slotted home his 19th goal of the season to put Cleethorpes ahead after just three minutes.
Robertson was denied a second goal for offside soon after before Sedge created a great chance when Josh Hope fed Andrew Wood and he squared the ball but Kieran Corley was denied by Steer.
Another Corley chance was blocked by a defender and from the resulting corner, Hope headed home but the effort was ruled out for a foul on Steer.
Tom Jackson’s curling effort was kept out by a diving Steer save but Liversedge levelled before half-time when Eli Hey capitalised on a Cleethorpes defensive error to slot home.
Liversedge cleared a Cleethorpes chance off the line and deserved to go into the break on level terms.
Wood fired an early second half free-kick agonisingly wide, before Steer again denied the striker.
Corley had a chance cleared off the goalline before Cleethorpes were reduced to 10 men when Hanslip received a second yellow card for a foul.
Despite being down to 10 men, Cleethorpes regained the lead in the 73rd minute when Cooper latched onto Heward’s long ball to curl home.
Heward was forced to leave the field following claims he was challenged late, off the ball, after his pass, which resulted in a melee straight after the goal.
Liversedge pressed looking for an equaliser but Cleethorpes broke and Roberton capitalised on a defensive error outside the area to grab his second goal and seal the home side’s win.