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Martin Carruthers doubled the home side's advantage midway through the second half, firing home from the edge of the box.
Carruthers grabbed his second of the contest with nine minutes left, Alex Calvo Garcia's 85th-minute header completing the rout.
The opening half was full off incident with Calvo-Garcia, Ian Kilford and Matt Sparrow all going close for Scunthorpe, while Richie Humphreys and Mark Tinkler enjoyed opportunities for Pool.
Pool should have taken the lead midway through the first period. However, Kevin Henderson was unable to profit from a bad Andy Dawson back pass, turning the ball wide of the target with the goal gaping.
That miss proved costly as Scunthorpe took the lead through Hayes.
Pool began the second half in positive fashion. Humphreys' firm left-foot shot was charged down by Wayne Graves, while Graeme Lee saw a header fly just wide and Kevin Henderson curved a shot wide of the post.
Scunthorpe weathered the storm and took control of the encounter as Carruthers grabbed his double and Calvo-Garcia added the fourth.
Tinkler saw a header rattle the woodwork late on but by that stage there was only one winner.