The home side deservedly took the lead on 13 minutes. Ian Stonebridge fed the impressive Tyson who crossed an inch-perfect ball and former Leicester hit-man Claridge slotted home for his first goal for his latest club.
Tyson then wasted a glorious chance two minutes later when he allowed himself to be robbed in the area. Promotion-chasing Scunthorpe resorted to roughhouse tactics as their offside trap kept falling foul of Tyson's pace.
Both Richard Kell and Matt Sparrow were booked for fouls, with Sparrow lucky to stay on the pitch after a disgraceful challenge.
Wycombe doubled their tally two minutes before the break. Gus Uhlenbeek picked up the ball and played in Tyson, and with the visiting defence ridiculously appealing for offside, Tyson slotted home his 13th goal of the campaign.
A bizarre decision by the referee meant that Sparrow wasn't sent off at the start of the second half following his second outrageous tackle of the game.
Claridge thought that he had put the game beyond the Iron reach when he slammed the ball into the net on 65 minutes, only for the celebrations to be curtailed by a linesman's flag for offside.
Scunthorpe substitute Paul Hayes tried to drag his side back into the game on 73 minutes, firing just wide from 20 yards.
Wycombe captain Roger Johnson was shown the red card on 75 minutes, leaving his side down to ten men following en elbow on Steve Torpey. From the resulting free kick Frank Talia made a brilliant save to deny Hayes.
Talia made another good save from a Peter Beagrie free kick on 85 minutes to preserve his side's advantage.
In what was a great irony, Sparrow, who should not have even been on the pitch, brought his side back into the game when he neatly finished past Talia on 87 minutes. However, the home side held on for the important three points.