A thrilling encounter saw Amar Purewal, Robbie Spence and Olly Martin score as Hebburn wrote their name into Tuesday’s play-off semi-final.
Pressure was in the air on the final day of the season, with Hebburn requiring at least a point or results to go their way to secure play-offs.
Player-manager Daniel Moore made several changes as himself, Arron Thompson and Joe Walton entered the starting 11.
Any nerves were quickly flattened out as Hebburn opened the scoring just three minutes into the fixture.
Moore played a long ball forward and a rush of blood came to the head of Cleethorpes keeper James McKeown, allowing Purewal to take it past the shot-stopper and roll it home.
And moments later, Hebburn almost found a second as another defensive error was capitalised by Martin but the foot of the post denied him.
On 13 minutes, Cleethorpes found an equaliser as Sam Topliss drove a neat strike into the bottom corner from distance.
The Owls again had a glimpse of goal when Harvey Tomlinson’s corner fell for Jack McMenemy to volley over at the back post.
With 21 on the clock, Thompson’s long pass dropped to Martin on the edge of the area and he hooked an effort over after some tricky footwork.
Hebburn number one Shaun Newbrook was hardly called into action all afternoon, the only exception being when Dan Gallimore fizzed a strike along the floor straight into the keeper’s path.
The Hornets had two chances after the 30 minute mark with Martin dragging an effort wide following a deflection, before Moore nodded over from Jack Hackett’s corner.
Former Grimsby keeper McKeown made a great save to deny Walton’s long shot before half-time, with a stop low to his bottom right.
Straight after the break, Hebburn found a second as Purewal received Tom Devitt’s throw-in and put a cross in for Spence to smash into the net.
There were no signs of slowing down as Purewal raced into the area and was tripped by substitute Josh Smaller, allowing Martin to step up and confidently dispatch the penalty.
Hebburn continued to attack in the second half but there was little goalmouth action, with Moore coming closest after heading over from a Spence corner on 78 minutes.
Following other results across the league, Hebburn will welcome Long Eaton United in the play-off semi-final on Tuesday night.
Hebburn Town: Newbrook, Devitt, Moore, Reid, Groves, Spence, Thompson, Hackett, Martin (McCamley 77’), Walton (Murray 63’), Purewal (Henderson 84’)
Unused subs: Harrison, Phillips
Goals: Purewal (3’), Spence (48’), Martin (53’)
Bookings: Martin (71’)
Cleethorpes Town: McKeown, Jamieson, Oglesby (Annan 63’), Topliss, Walker (Smaller 13’), Richards, Tomlinson (Essel 72’), Gallimore, Bateson, Flett, McMenemy
Unused subs: Parr, Lowe
Goals: Topliss (13’)
Bookings: Smaller (53’)
MOTM: Jake Hackett
Referee: Jonathan Gill
Attendance: 619