With Liam Dickens and Lawrence Heward unavailable, Tim Lowe and Nick Goodwin paired up in central defence in the only changes from Saturday's defeat at Clipstone in the FA Cup.
The Owls got off to the worst possible start, falling behind in just the second minute. Jody Barford did well to save from Lewis Chambers shot but the Cleethorpes defence dithered allowing Liam Morris a simple tap in from the rebound.
Cleethorpes then enjoyed a sustained period of pressure. Peter Winn headed just over before Darren Hanslip's header was tipped over the bar by Rainworth goalkeeper Nathan Burrows. Nick Goodwin tested Burrows with a header before the Owls Danny Trott found himself one on one with the keeper but saw his powerful shot cannon agonisingly back off the underside of the cross bar.
The Owls were getting the feeling that it wasn't going to be their night and were further stunned as the hosts scored twice in two minutes to take a 3-0 lead with just 21 minutes played. Defender Matt Plant made it 2-0 with a sweetly struck volley before Matt Thompson's low cross wasn't dealt with by the Clee defence, allowing Morris another simple tap in from close range.
The shocked Cleethorpes players resorted to hitting long, direct balls straight down the throats of the home defenders which were easily dealt with. The Owls were then given a glimmer of hope of staging a comeback as Peter Winn hit a stunning strike from 25 yards to reduce the arrears, the power of the shot meant that Burrows could only push it into the roof of the net.
Hopes of a comeback were quickly dashed however as midfielder Sam Dockwray fired home from the edge of the box to give Rainworth a 4-1 half time lead.
Marc Cooper shot tamely at Burrows at the start of the second half before Hanslip headed over from Winn's corner. Goodwin's header then clipped the top of the cross bar as the Owls pressed. Cooper made the score 4-2 in the 63rd minute, heading home from close range.
Chances came and went at both ends as Rainworth's Lewis Bingham was twice denied a goal, heading over the bar when finding himself completely unmarked in the penalty area before a great block by Tim Lowe denied him a shooting opportunity. At the other end, a great volley by substitute Reece Newell was cleared off the line by the home defence.
Bingham wasn't to be denied for long however as he found himself clean through on goal after 74 minutes before coolly lobbing the ball over Barford to make the score 5-2.
The Owls reduced the arrears in the final minute as sub Jack Richardson nodded in from inside the six yard box. Rainworth still found time to net again though, Clee appeals that Rainworth goalkeeper Burrows had carried the ball over his own goal line were waved away and a quick break allowed Bingham to score with another lob, a goal that was almost a carbon copy of his first effort.
The referee blew the full time whistle just seconds later to put Clee out of their misery. The Owls remain in 21st place in the Toolstation NCEL Premier Division table and are still looking for their first points of the season. More worryingly, the team has conceded 10 goals in the last two away league games.