The former Millwall and Oxford striker fired the Shots into a 38th-minute lead with his second goal for the club.
Henry grabbed another after 58 minutes following good work by Tyler Frost and Hady Ghandour.
Latics struck back immediately as Reagan Ogle’s cross deflected in off Frost.
But Frost turned from villain to hero by converting Ashley Akpan’s 68th-minute cross.
Theo Widdrington’s stoppage-time penalty rounded off an impressive success after Ghandour’s close-range attempt had been handled.
Boss Micky Mellon said: "I want to apologise to the supporters who came down.
"I don't want to do that too many times on behalf of us all.
"Defensively we were poor, gave away too many really cheap goals and you're going to make it very difficult for yourself if that happens."
Mellon's men will hope to bounce back tomorrow (Monday) when they host Gateshead (3pm).
