The Pilgrims led 1-0 at the Jakemans Community Stadium courtesy of Rhys Smaller's early breakthrough.
Farsley powered back either side of half-time to lead 3-1, only for Jake Thompson to reduce the arrears late on.
Boston: Austin Barker, Finley Hipkin, Sean Bray-Smith (Denis Matei 80), Charlie Brooks, Kirils Snikeris, Josh Panton (Jake Thompson 60), Rueben Fogg, Toby Cotton, Will Pettitt, Daniel Bridges (Will Langford 65), Rhys Smaller. Subs (not used): Finley Ging, Dan Martin (gk).
Referee: Istvan Mod.