A fine looping header from debutant Ahkeem Rose in the 23rd minute and Nathan Arnold's third goal in four appearances in the 71st minute secured all three points for the Pilgrims.
United's fast start at Edgeley Park was rewarded to the maximum, with Nicky Walker particularly prominent in attack and the recalled Ben Middleton outstanding at centre-half.
Middleton’s inclusion from the start was one of five changes made by manager Craig Elliott, with Spencer Harris and Grant Roberts ruled out through injury and Jordan Gough through suspension.
Rose and fellow Grimsby Town loanee Max Wright were included from the start and both players contributed heavily to United’s vibrant start.
The visitors took the lead just past the mid-point of the first half when Walker worked a yard of space to cross from the left and ROSE looped a tremendous header into the far corner beyond the reach of keeper Ben Hinchliffe.
United almost doubled their lead when Middleton planted a header wide following Arnold’s corner delivery.
The Pilgrims were indebted to captain George Willis for preserving their lead when he produced a fine point-blank save to deny Nyal Bell after United had failed to clear a set-piece into their box.
County, switching to three at the back, were a stronger proposition after the break and Ben Davies and Ryan Qualter had to repel teasing crosses from rampaging wing-backs Adam Thomas and Scott Duxbury respectively.
United suffered a double injury blow when Rose left the field with cramp and Andi Thanoj followed with a hamstring niggle. Blackpool loanee Yusifu Ceesay and Jonathan Wafula deputised from the bench.
Willis made a fine stop to keep out Bell’s rising drive and it laid the platform for United to double their lead in their next attack when Walker and Ceesay combined to allow ARNOLD to round Hinchliffe and fire home from a tight angle on his left foot.
Stockport tried to respond, with Sam Walker firing a 25-yard free-kick off target and sub Matt Warburton seeing a low drive deflect marginally wide off Ben Davies.
United could even have extended their lead with Wafula glancing Davies’ free-kick wide and Walker being denied at the death by keeper Hinchliffe.
Stockport (4-2-3-1): Ben Hinchliffe; Adam Thomas, Ashley Palmer, Chris Smalley (Scott Duxbury 46), Dan Cowan; Jordan Keane (Sam Minihan 77), Sam Walker; Frank Mulhern (Matt Warburton 73), Connor Dimaio, Darren Stephenson; Nyal Bell. Subs (not used): Jordan Downing, Ian Ormson (gk).
Boston (4-4-2): George Willis; Ben Davies, Ryan Qualter, Ben Middleton, Ashley Jackson; Max Wright, Brad Abbott, Andi Thanoj (Jonathan Wafula 63), Nathan Arnold (Toby Lees 90); Ahkeem Rose (Yusifu Ceesay 60), Nicky Walker. Subs (not used): Adam Marriott, Jonny Margetts.
Referee: Adam Herczeg.
Attendance: 3,050 (101 visitors).