The Reds took the lead in the 17th minute through captain Tom Kearney's deflected free kick after Shaun Whalley had been fouled 25 yards from goal.
New signin Jefferson Louis then went close after being set up by Simon Brown, but Brian Little's side failed to add to their tally before the break.
After the re-start, Wrexham extended their lead when Louis headed home from a corner on 66 minutes, after Stevenage had been reduced to ten men following Steve Morison's challenege on Darran Kempson.
But the Reds were reduced to 10 men shortly after when Levi Mackin was dismissed for a second bookable offence.
However, Wrexham didn't lose momentun and Shaun Whalley put the Reds three up on 71 minutes after being set up by Sam Aiston.
Substitute Christian Smith added the Reds' fourth from a corner with five minutes remaining, before fellow sub Marc Williams capitalised on a mix-up in the Stevenage defence to complete the rout.
The result capped a perfect afternoon for Little, who will be hoping his side can build on their good start to life outside the Football League.
Wrexham: Ward, Spender, Kempson (Steve Evans, 75), Nat Brown, Tremarco, Simon Brown, Kearney, Mackin, Aiston, Louis (Marc Williams, 83), Whalley (Smith, 72).
Subs not used: Baynes, Anthony Williams
Attendance: 4,901
Don't miss Monday's Evening Leader for a full match report.
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