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Richard Cresswell had already grabbed his ninth of the season when Montgomery found the target to end a miserable sequence of two wins in ten, Cresswell killing off Ian Holloway's side on 66 minutes.
The Sheffield side got off to a dream start with just 45 seconds gone. Mark Yeates curled in a teasing corner from the right, the ball was flicked on and, as Blackpool tried to clear, Cresswell struck from close range.
United almost had a second as Henri Camara beat Matthew Gilks in a chase at the near post, the ball fell nicely for midfielder Stephen Quinn who lashed in a low strike that was blocked by the Blackpool keeper six yards out.
Blackpool had claims for a penalty waved away by referee Oliver Langford after Charlie Adam was sent tumbling following a challenge from Marcel Seip, Keith Southern hammering the loose ball inches wide of the target.
United grabbed a second goal two minutes before the break. It was carved out by the pacy Camara. The ex-Wigan striker cut inside from the left flank picking out Montgomery, who drilled his low shot from 20 yards into the bottom left-hand corner.
Emergency loan signing Paul Connolly foiled Blackpool after Adam's looping effort left Mark Bunn stranded, the Derby defender hooking the ball from under the bar under pressure from Jason Euell.
Cresswell hit a third in the 66th minute, Darius Henderson firing in a low cross from the left across the face of the goal with the ex-Stoke striker adding the finishing touch.