The 23-year-old claimed his first competitive Pilgrims goal with a rising 25-yard strike that flew past Shots goalkeeper Glenn Morris.
Argyle took just 34 seconds to open the scoring. Nick Chadwick's deft flick to Joe Lennox sent him away down the right and the winger's inch-perfect pass was converted from close range by Paris Cowan-Hall.
The visitors allied to level with 12 minutes on the clock, Craig Reid pouncing on Peter Vincenti's blocked shot to rifle home.
Reid then hit the post in the 17th minute after Troy Brown's header came back off the bar.
Gurrieri then stole the show, striking the woodwork before providing a quality finish to give the hosts a lead they would not relinquish.