The Pilgrims had the better chances during a goalless first half but found themselves 2-0 down by the mid-point of the second half courtesy of strikes from Darren Stephenson and Elliot Osborne.
Ben Davies reduced the arrears from the penalty spot in the 77th minute but Frank Mulhern wrapped up all three points for the title chasers with a sublime third four minutes later.
United more than matched their high-flying hosts during an enterprising first half display and went close within three minutes through debutant Jake Wright, who forced Ben Hinchliffe into a smart save.
County’s top goalscorer Matt Warburton drifted an effort across goal and wide as Stockport threatened for the first time.
The chance of the half fell to Gavin Allott when he met Max Wright’s pinpoint cross from the right — only to bullet his header over the crossbar on the six-yard line.
Hinchliffe also made a low save to claw aside Ryan Qualter’s header late in the half following Nicky Wroe’s corner to the back post.
Stockport took a 55th minute lead when Dan Cowan crossed from the County right and STEPHENSON hooked home an acrobatic finish from six yards.
The Hatters doubled their lead on 66 minutes when OSBORNE rammed home the loose ball after seeing his initial effort parried by George Willis, having only emerged as a substitute a minute earlier. United protested in vain for a foul on Davies in the build-up.
The Pilgrims got themselves back in contention when Paul Turnbull was penalised for handling Andi Thanoj’s pass and DAVIES crashed the resulting spot-kick down the middle.
County, however, re-asserted their two-goal lead four minutes later when MULHERN curled home a beauty from 20 yards after being teed up by full-back Scott Duxbury.
United introduced Jonny Margetts for his first appearance since September, following the completion of loan spells with Gainsborough Trinity and Matlock Town, but the Pilgrims were unable to cut the deficit in the closing stages as County extended their unbeaten run into a 23rd competitive match to go top of the table in the process.
Boston (4-4-2): George Willis; Ben Davies, Ryan Qualter, Ben Middleton, Ashley Jackson; Max Wright (Jay Rollins 83), Nicky Wroe (Brad Abbott 86), Andi Thanoj, Nicky Walker; Gavin Allott, Jake Wright (Jonny Margetts 83). Subs (not used): Jonathan Wafula, Spencer Harris.
Stockport (4-2-3-1): Ben Hinchliffe; Dan Cowan, Jamie Stott, Ashley Palmer (Sam Walker 53), Scott Duxbury; Jordan Keane, Paul Turnbull; Adam Thomas, Matt Warburton (Elliot Osborne 66), Darren Stephenson (Jake Kirby 86); Frank Mulhern. Subs (not used): Sam Minihan, Ian Ormson (gk).
Referee: Amy Fearn.
Attendance: 1,073 (263 visitors).