Plymouth took the lead in the 16th minute when keeper David Button's free-kick from deep inside his own half was headed on by recalled target man Rory Fallon and into the path of Wright-Phillips. The in-form front man wasted no time in making the best of it either, clinically ramming home from just inside the area.
Argyle's joy was shortlived, though, as the Terriers levelled within two minutes. Liam Ridehalgh sent winger Graham Carey away down the left and his cut-back cross from the byline was superbly converted at the far post by an unmarked Antony Pilkington, who crashed the ball past Button.
Argyle countered with right-wing Craig Noone looping a header on to the bar from full-back Onismor Bhasera's deep cross from the left.
Fallon had a headed effort ruled out for pushing in the 54th minute but played a part in Argyle restoring their lead 12 minutes later.
It was a route-one repeat of the opening goal. Button cleared long from his penalty area, Fallon stooped to help the ball on into the path of Wright-Phillips, and he calmly slid the ball home for his seventh goal of the campaign.