Slocombe, 21, was thrown on when Joe Murphy was sent off in the 62nd minute for handling outside his box.
It was 1-1 at the time but Blackpool preyed on Slocombe's inexperience.
Charlie Adam soon thrashed a free-kick past the youngster, who then spilled Stephen Crainey's cross to gift Ben Burgess a tap-in.
Alex Baptiste rifled a long-range drive past the keeper in the 89th minute.
Adkins said: "Sam says their striker trod on his elbow for the third and that caused him to drop the ball, but he is a good character and will have enjoyed today.
"It was a crazy five minutes that changed the whole complexion of the game. Our keeper was outside the area, made a reactive stop and was sent off."
Scunthorpe had taken the lead in the 51st minute with Paul Hayes lifting a shot over Matt Gilks, but Ian Evatt levelled with a header from Baptiste's cross.
Seasiders boss Ian Holloway said: "We weren't in the first half but we scored four fantastic goals."
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