Spennymoor took the lead with 42 minutes played when David Foley wriggled free to blast a ball across goal which was touched home by Glen Taylor under pressure from Brad McGowan.
The Pilgrims came alive after the break, with Kabongo Tshimanga’s drive deflecting over and Chris Chantler superbly clearing off the line to deny Brad Beatson.
Tshimanga lifted another effort over the bar following Taron Hare’s cross, while Ashley Hemmings’ in-swinging corner rattled the post, before visiting keeper Dan Lowson denied Tshimanga and substitute Karl Hawley in quick succession.
Spennymoor effectively killed the contest on 74 minutes when Foley found Taylor who, after neatly turning Jordan Keane, fired low past an exposed Willis.
It was well and truly game, set and match in the 89th minute when Rob Ramshaw and Foley teed up Andrew Johnson to roll home number three.