The Pilgrims were 3-1 victors over York City on the main pitch at the Jakemans Community Stadium.
Thompson's goal, scored in the 85th minute, ensured United edged ahead of FC Halifax Town at the foot of the table in the final standings.
Boston: Austin Barker, Finley Hipkin, Oliver Houlston, Kirils Snikeris, Finley Ging, Will Langford, Will Pettitt (Charlie Brooks 60), Jake Thompson, Rueben Fogg (Zac Hardy 85), Toby Cotton (Josh Panton 70), Rhys Smaller (Sam Finch 80). Sub (not used): Daniel Bridges.
Referee: Istvan Mod.