Mark Jones' fourth minute own goal put the Pilgrims on the back foot and their woes were compounded 11 minutes later through Michael Spillane.
Town put the game to bed eight minutes after half-time when Jake Reed lobbed Henrich Ravas to score the hosts' third goal.
The Pilgrims had suffered a double blow before kick-off with Sunderland loanee Dylan McEvoy and top goalscorer Dayle Southwell both ruled out through injury.
There had been little sign of things to come though and Town were soon in front. Robert Eagle's corner was inadvertently converted by JONES with a flying header.
Things got worse on the 15-minute mark with SPILLANE smashing past an exposed Ravas after United had failed to clear another Eagle flag-kick.
There was a massive chance for Town to go 3-0 up but Rossi Jarvis cleared the crossbar from the edge of the box when well-placed, while Ravas thwarted Reed from close-range.
Dennis Greene rang the changes at half-time, with John Sands, Lewis Hilliard and Cameron Johnson all entering the fray.
Hilliard's curling shot was held by Ben Killip following good play down the left from fellow sub Sands, but Town soon went three goals to the good.
REED latched on to a long ball over the top from Spillane to nip in between Ravas and Mills to lob home into an unguarded net eight minutes into the half.
Chances were at a premium thereafter, with the game in the bag for Town, although the hosts did go close again when Bradley Woods-Garness' drive was saved by Ravas and Ryan Jarvis' follow-up was scrambled to safety.
There was almost late cheer for the Pilgrims, but Norwich City loanee Killip produced an unbelievable save to claw Sands' top corner header away from the target.
Lowestoft (4-4-2): Ben Killip; Harry Barker (Adam Smith 79), Jack Ainsley, Michael Spillane, Robert Eagle; Harvey Hodd (Dean Mason 63), Rossi Jarvis, Andrew Fisk, Ryan Jarvis; Jake Reed (Bradley Woods-Garness 74), Shaun Bammant. Subs (not used): Chris Henderson, Jake Jessup (gk).
Boston (4-4-2): Henrich Ravas; Liam Marrs (Cameron Johnson 46), Zak Mills, Carl Piergianni, Jordan Richards; Kaine Felix, Scott Garner, Grant Roberts (Lewis Hilliard 46), Jay Rollins; Mark Jones, Ryan Robbins (John Sands 46). Sub (not used): Jason Alexander (gk).
Referee: Carl Fitch.
Attendance: 696.