First half goals from Jimmy Knowles and Tom Leak did the bulk of the damage for the Pilgrims, with Jordan Richards adding a clinching third with eight minutes to play.
The only blot on United's copybook was a first half injury sustained by midfielder Martin Woods.
The Pilgrims started at a fast tempo, with Deji Sotona and Knowles seeing early efforts deflected off target.
United took a 15th minute lead when Michael Gyasi, making his first league start for the Pilgrims, teed up Ethan Sephton to cross from the left and KNOWLES drilled home at the back post after Emmanuel Oke had failed to head clear.
Woods was withdrawn in the 24th minute, with Zak Mills deputising, but it took only three more minutes for United to double their lead, with LEAK heading home Sotona's free-kick delivery.
Gyasi subsequently tested Jack Giddens in the Stortford goal, while Kelsey Mooney cracked an effort against the crossbar following Jai Rowe's excellent ball from the right.
Sotona was denied by a Riccardo Di Trolio goalline clearance within a minute of the restart, but the second period was a half of few chances.
Adam Marriott was introduced as a late sub, following his midweek arrival on loan from Bromley, and he forced Giddens into a smart save with a late free-kick, with the Stortford keeper also denying Rowe spectacularly in stoppage time.
By this time, United were three goals to the good after Giddens kicked the ball straight to RICHARDS, who returned it over the keeper's head and into an empty net from 30 yards.
Boston (4-4-2): Aaron Chapman; Jai Rowe, Michael Bostwick, Tom Leak, Ethan Sephton; Michael Gyasi (Sam Smart 74), Jordan Richards, Martin Woods (Zak Mills 24), Deji Sotona (Adam Marriott 79); Jimmy Knowles, Kelsey Mooney. Subs (not used): Brad Nicholson, Keaton Ward.
Bishop's Stortford (4-1-4-1): Jack Giddens; Amadou Kassarate, Harry Beadle, Sam Robbins, Riccardo Di Trolio; Emmanuel Oke (Lordon Akolbire 46); Darren Foxley (Jack Thomas 75), Gio McGregor (Ryan Charles 69), Kane Crichlow, Aaron Greene; Zain Walker. Subs (not used): Tosin Olufemi, Fraser Alexander.
Referee: Nathan Oakes.
Attendance: 1,735 (55 visitors).
PIC: Tim Hoff.