The home side took the lead inside the opening 10 minutes when Wolves failed to clear from a corner, allowing Kirk Millar to fire in from close range.
The newly-promoted Championship side soon began to dominate possession and were back on level terms in the 24th minute, when Leon Clarke collected the ball from Liam McAlinden before slotting in for his second pre-season goal this year.
McAlinden found the target himself four minutes later when Shamrock goalkeeper Craig Hyland miscontrolled a backpass, allowing the striker to slot into an empty net.
Wolves almost extended their lead at the start of the second half when Nouha Dicko crossed the ball into the box only for Hyland to parry away, before Bakary Sako tried to flick in from the rebound, but missed the target.
Hyland continued to come under pressure in the Shamrock goal, eventually letting in a third when Dicko guided a delicate shot into the far corner.
Carl Ikeme had to make a couple of saves late on as Shamrock tried couple ambitious shots, but the Wolves keeper was able to prevent them getting back into the match.
Sako managed to get on the scoresheet in the final minute of the match when Michael Jacobs was brought down in the box by Robert Bayly, allowing the winger to smash the ball home from the penalty spot, completing an emphatic win for the visitors.