The Stockport County attacker made the breakthrough in the 86th minute to settle a scrappy encounter at Edgeley Park as the hosts bolstered their play-off hopes.
United were not unduly troubled throughout but were eventually undone when Stockport struck in the dying moments.
Jonathan Wafula had been handed his full debut ahead of kick-off, with Jay Rollins sidelined with a persistent groin injury.
Warburton, James Ball and Jason Oswell all went close for Stockport during the opening stages while United’s best first half chance fell to Reece Thompson, who engineered a yard of space but dragged his effort across goal and wide.
County ramped up the pressure after the break as they attacked the famous Cheadle End and Ryan Qualter and Jamie McGuire made spectacular blocks to keep the hosts at bay.
Home keeper Ben Hinchliffe produced a fine save with his legs to deny Thompson but County stole all three points when WARBURTON steered the loose ball past Jon Stewart after Scott Duxbury and Darren Stephenson had linked up down the hosts’ left-hand side.
Stockport (3-4-1-2): Ben Hinchliffe; Dan Cowan (Darren Stephenson 75), Michael Clarke, Jamie Stott; Adam Thomas, Harry Winter (Paul Turnbull 64), James Ball, Scott Duxbury; Rhys Turner (Stephen O’Halloran 88); Jason Oswell, Matt Warburton. Subs (not used): Sam Minihan, Ian Ormson (gk).
Boston (4-4-2): Jon Stewart; Wes Atkinson, Ryan Qualter, Jordan Keane, Stephen Brogan; Jonathan Wafula (Gregg Smith 88), Brad Abbott, Jamie McGuire, Ashley Hemmings; Reece Thompson, Jake Beesley (Benny Igiehon 80). Subs (not used): Kabongo Tshimanga, Taron Hare, George Willis (gk).
Referee: Garreth Rhodes.
Attendance: 2,244 (37 visitors).