The Pilgrims trailed to Adam Morgan's 18th minute header but came roaring back after half-time, with Gregg Smith particularly excelling up front.
Nicky Walker, Ahkeem Rose and Max Wright struck in the 64th, 73rd and 90th minutes to seal a fourth away win of the campaign.
United boss Craig Elliott had gone back to an experienced XI, with Grimsby Town loanees Rose and Wright relegated to the substitutes’ bench.
The Pilgrims twice went close through Smith headers in the opening stages, but both efforts dropped off target following deep Ben Davies deliveries from the right.
The Nash, without a home win to their credit all season, took the lead when Oliver Crankshaw delivered a pinpoint cross from the right which was powered home by the head of MORGAN at the back post.
United came close to an equaliser after the break when Ryan Qualter nodded narrowly too high from a Davies corner.
The game’s defining moment arrived when Morgan found himself with a clear sight of goal but rolled the ball wide of George Willis’ left-hand post.
The Pilgrims capitalised immediately and Smith’s deft header sent WALKER galloping through to beat Cameron Mason with aplomb.
Mason plucked a Davies free-kick out of the air while Willis had to be alert to make a flying save to deny Crankshaw as the Nash threatened to re-establish their lead.
United edged ahead with 17 minutes remaining when ROSE swiveled neatly to finish at the near post after Curzon had failed to clear Davies’ corner.
Brad Abbott slammed an effort wide in the closing stages before Mason denied Rose with his legs, but it was left to WRIGHT to apply the icing to United’s cake with a prodded finish from 12 yards after waltzing through the home rearguard.
Curzon (4-4-2): Cameron Mason; Danny Morton, Jonathan Hunt, Mo Ali, Cameron McJannet; Oliver Crankshaw, Paul Marshall (Chris Rowney 74), Joe Guest, Connor Hughes (Ryan Brooke 90); Niall Cummins (Alex Samizadeh 68), Adam Morgan. Subs (not used): Mason Fawns, Danny Shaw.
Boston (4-3-3): George Willis; Ben Davies, Ryan Qualter, Ben Middleton, Ashley Jackson; Brad Abbott, David Norris (Ahkeem Rose 59), Spencer Harris; Jonathan Wafula (Max Wright 59), Gregg Smith, Nicky Walker (Jordan Gough 90). Subs (not used): Andre Johnson, Adam Marriott.
Referee: Aaron Jackson.
Attendance: 305.