Karl Fitzpatrick's high ball was flicked by David Hodgson into the path of Wilshere for his first before neat footwork set up his second.
Winger Henry Fa'afili went over early in the second half to give the Wolves hope but Hodgson replied for the Reds.
Junior Langi's late close-range score rounded off a great day for Salford.
Salford coach Karl Harrison: "Our three first-choice half-backs were unavailable through injury but I
thought David Fitzpatrick and John Wilshere were outstanding.
"We've got a great bunch of blokes and I'm just really pleased, particularly with the players we had out.
"We were written off before we came here but our front row was outstanding and easily matched Warrington's."
Warrington: Grose, Fa'afili, M. Gleeson, Kohe-Love, Reardon, Briers, Sullivan, Leikvoll, Clarke, Rauhihi, Swann, Westwood, Parker. Replacements: Bridge, M. Gleeson, Wood, Lima.
Salford: Hodgson, Langi, Littler, Moule, Stewart, Wilshere, Fitzpatrick, Coley, Alker, Highton, Brocklehurst, Sibbit, Finnigan. Replacements: Jonkers, Haggerty, Clough, Baldwin.
Referee: R Laughton (Barnsley)
MMIX
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