The 23-year-old touched down seven minutes into the first half and 16 into the second as Glasgow ground the Italian outfit down after the interval to record a bonus-point win.
McGuigan responded to Dries van Schalkwyk's early try as did Alex Dunbar to Tito Tebaldi's effort before a second from the wing and additional scores from James Eddie and Peter Murchie.
Glasgow fly-half Scott Wight and Finn Russell converted two each, while the former also kicked a penalty, with Daniel Halangahu contributed ten points for winless Zebre.
Wright saw his early move cleared by Zebre for lineout before the Italian team opened the scoring when Niko Matawalu's long pass out was picked off by van Schalkwyk.
The Zebre No.8 outpaced everyone to score with fly-half Halangahu slotting the conversion to put the hosts 7-0 ahead after just five minutes - however Glasgow responded in style.
Wing McGuigan showed great hands to leave the Zebre for dead and score under the post before Wight ensured the scores would be levelled with the conversion.
With just nine minutes on the clock the match had its third try and the second from Zebre as Wight's kick was charged down by full-back Tebaldi, who picked up and scored.
Halangahu converted only for Glasgow to once again respond immediately with more great work from scrum-half Matawalu, this time in the loose, which Dunbar took full advantage of.
Wight maintained the 100 per-cent kicking record for the game as he converted to make it 14-14 after 12 minutes before slotting a penalty as the Warriors took the lead for the first time.
After ten minutes without a score Halangahu slotted a penalty after Glasgow were caught offside to level the scores however his 100 per-cent record was to end moments later.
Halangahu slotted a penalty wide in the 29th minute but didn't fail with another effort right in front of the posts just before the break as Zebre headed in leading 20-17.
Glasgow lost Graeme Morrison to a yellow card two minutes into the second half while Filippo Ferrarini, moments after replacing Filippo Cristiano, following suit.
Zebre were then under intense pressure from the Warriors with their pack held up over the line after a quick tap and go from the lively Matawalu.
And Glasgow got the try their efforts deserved in the 56th minute as McGuigan claimed his second of the afternoon after latching onto a pass, albeit a wayward one, from Ryan Wilson.
Russell, who had just replaced Wight, lined up the conversion but fired it wide with Halangahu following suit after Zebre were awarded a penalty in Glasgow's 22 in the 58th minute.
And the Warriors made Halangahu pay on the hour as Matawalu carved out another opportunity before feeding Eddie on the wing for the visitor's fourth try and the bonus point.
He was at it again as Glasgow picked up a fifth try late on combining with Sean Kennedy and Tim Swinson to set up Murchie with Russell slotting his second conversion.
|Zebre Score Card|
|Dries van Schalkwyk||1||5|
|Glasgow Warriors Score Card|