The victory sets up a final against Spalding United on a date and at a venue yet to be confirmed, with Scunthorpe now looking to win the competition for the second time in three seasons.
Jimmy Dean named an all-changed XI for the encounter, making wholesale changes to give opportunities for the remainder of the squad to get minutes and stake a claim for the shirt. The line-up included first starts for loanees Flynn Clarke and Dylan Youmbi, while First Team Coach Andy Butler made his second appearance in the competition in the heart of the United defence.
Scunthorpe's bench included options from the starting team from the win over Alfreton Town, providing suitable alterations should the side require it.
Cleethorpes had the first opportunity of the game from their kick-off, with a deflected long range effort barely troubling York City loanee Maison Campbell.
The pendulum quickly swung towards the Iron's favour though as they won the first corner of the game following a free-kick which was worked between Michael Kelly and Clarke, who saw his cross headed behind.
Scunthorpe youth product Dan Gallimore, now playing for the Owls, was next with an effort on goal, but his rolled shot went across the area and wide of Campbell's right-hand post.
For their next chance on 10 minutes, the Iron went route one from a Campbell goal kick. His punt forward was knocked on by Danny Whitehall to Cameron Wilson, who lifted his shot over the goalkeeper, but also over the crossbar from a wide left position inside the area.
United were starting to make further inroads and, following a sweet first touch from Kelly, he sent in Whitehall down the left. Wilson received the ball next before teeing up Beestin, but his shot flew over the bar from 20-yards out.
Ross Barrows and Youmbi were next to get involved, this time down the right, on 20 minutes. Clarke and Beestin took over before Youmbi's cross was turned away from danger by the home defence.
Wilson and Beestin continued to be threats on the Cleethorpes goal, and following a near Butler chance on goal, it would be the duo that would combine for the deadlock breaker on 26 minutes. Wilson brought the ball down the left before cutting onto his right foot. He shaped to shoot as he dribbled the ball across the edge of the box, but instead opted to roll the ball back with the bottom of his foot to Beestin, who sweetly drilled an effort from 20-yards past the home shot stopper to give the Iron a deserved lead.
Five minutes later, and Cleethorpes thought they were level, but for a superb one-handed save to Campbell's right following a first-time effort from close range.
That equaliser did come in the next attack on 39 minutes, as play continued with Youmbi on the deck. Cleethorpes drove down the left and sent in an inviting cross for Adamson, who bundled the ball past Campbell.
With the scores locked in a stalemate, the Iron kicked off the second half looking to take the lead for the second time in the game. Nearly 15 minutes passed without any action, leading to the United boss making a treble substitution, introducing influential players to the ranks.
It was a starter who made the Iron's next chance though, with Norwich City loanee Clarke winning a throw before the next move saw a ferocious drive draw the Owls shot stopper into a fine save, which he gathered at the second attempt under pressure from substitute Dion Sembie-Ferris.
It was the substitute who made the next attack on 65 minutes, driving forward before seeing his dink headed away. The loose ball was picked up by Ross Barrows, but the effort flew over.
Scunthorpe were pressing for the goal to see them in front again, with Campbell's route one kick again sent forward to an Iron body. Clarke and Kelly both combined to win a corner, before a right-winged free-kick is awarded. That cross was knocked back across goal, with Kouogun seeing his effort blocked, and Clarke's shot suffered the same fate.
With the Owls looking to run down the clock, one played saw yellow for excessively doing so, with the next player in the referee's book soon after as Beestin was cynically brought down on the left channel.
From the resultant free-kick, chested down by Elliott, Beestin struck a thunderous effort just wide, which took the slightest of touches from a defender for a corner.
It was from that corner, in the 77th minute, that the Iron went back ahead again. Barrows was twice denied with efforts inside the box, but the ball fortuoutously fell to Beestin at the near post, who rolled an effort into the net in front of the travelling Iron contingent.
The lead could have been doubled a minute later had the referee agreed with the vociferous penalty shouts from behind the goal for an alleged handball, but the official in the middle opted to let play continue.
Flynn Clarke had the game's last effort in the 89th minute, sending an effort over after more good work from Sembie-Ferris, with the Iron comfortably seeing out the four additional minutes indicated to book a place in the final.
IRON: Campbell, Kelly, Kouogun, Beestin (Ogle, 90), Wilson (Sembie-Ferris, 58), Pugh, Clarke, Youmbi (Scales, 58), Butler, Barrows, Whitehall (Elliott, 58).