It was their biggest home win of the season against a Posh side that is now looking doomed to the drop back to League One,
Posh were torn apart at the back by a terrific attacking display by Scunthorpe in the first half in which they scored three times and might easily have doubled their tally.
Scunthorpe opened the scoring in the 15th minute with a cracking effort. Matt Sparrow won possession in midfield and fed the ball through for striker Paul Hayes who raced into the box and rifled it like a bullet from a narrow angle into the top far corner of the net past a startled keeper Joe Lewis.
They struck again ten minutes later when Hayes turned provider, sending Garry Thompson racing through to beat Lewis with a right-foot shot for his second goal in successive games.
And Scunthorpe struck again on the stroke of half-time when skipper Sam Togwell tried his luck from 25 yards with a shot which flashed past Lewis and into the net off the foot of a post.
Peterborough had mustered nothing in reply and it became a damage-limitation exercise for Jim Gannon's men.
They did shape up better in the second half but it was Scunthorpe that struck again after 64 minutes when Thompson exchanged passes with Hayes before slotting home his second goal of the game past Lewis.
He should have completed his hat-trick in the closing minutes but missed an easy near-post chance set up by substitute Donal McDermott.
It was an easy win for Scunthorpe who had centre-back Kenny Milne making his first start for over 18 months after recovering from a knee injury.
Posh were denied a consolation goal when striker Craig Mackail-Smith had a close-range header well-saved by goalkeeper Joe Murphy.