The Welsh side were rarely in the game and once they went two goals down they lost their appetite completely.
The Red Dragons escaped an early penalty scare with a strong appeal for a handling offence and then midfielder Richard Kell got forward twice to fire over the visitors' bar.
Juan Ugarte almost grabbed his first FA Cup goal in the 12th minute when Chris Llewellyn lifted the ball into the box for the Spaniard, who quickly turned to force Paul Musselwhite to tip the ball over the bar.
But two minutes later the Welshmen were in arrears, the skills of Peter Beagrie were to the fore as he crossed into the box and young defender Lee Ridley looped the ball over Matt Baker - though it was helped by a deflection.
Ugarte then followed up with two more attempts, one flying wide, while the second was blocked by Ridley.
Scunthorpe were quickly out of the traps in the second-half and they grabbed another goal in the 53rd minute, which virtually killed off struggling Wrexham.
Paul Hayes cracked in a shot which was only parried by Baker, he really should have held the ball but Matty Sparrow was on hand to tap in at the right-hand post.
Pressure continued to build on Wrexham and teenage midfielder Andy Butler headed firmly against the bar and then substitute Cleveland Taylor raced through to blast in a shot which Baker stopped at point-blank range.
The game was definitely out of Wrexham's reach and they almost conceded a third goal when Hayes got through and headed another effort against the crossbar.
The result left dreaming of a glamour tie in the third round, and Wrexham merely dreaming of surviving after being placed in administration.
The £700 raised by Iron fans before the game, and presented to the Wrexham Supporters Trust, is a drop in the ocean of their debt but everyone connected with Scunthorpe wishes them well in their battle against club owner Alex Hamilton and their bid to wrest control from him.