Brian Laws' Iron were leading by two goals when Prutton was dismissed and they added two more goals in the second half against a young and injury-hit Walsall side, now themselves without a win in nine games.
The visitors took control from the start in Tuesday night's League One encounter and went ahead in the 13th minute when a Mark Duffy corner was headed in at the far post by central defender Niall Canavan.
The visitors added a second on 30 minutes when Duffy tapped in after Hawley's shot had been blocked.
However, a minute from the half-time interval, Scunthorpe midfielder Prutton was red carded for a crunching tackle on Adam Chambers.
But, despite this, the visitors scored twice more in the second half, another Canavan header from a Duffy corner on 50 minutes before Leon Clarke added his 8th of the season, chipping keeper David Grof on 75 minutes.
Substitute Will Grigg grabbed a consolation goal for Walsall in the last minute as their fans sounded their frustration.
