The Pilgrims led through Jordan Thewlis' 20th minute spot-kick following a foul on Martyn Woolford and their cause was boosted further after the break when home striker Owen Watkinson was sent off for elbowing Tyrell Warren.
Curzon levelled with six minutes to play when Andrew Halls converted from the spot following a foul on Mike Calveley.
United boss Craig Elliott had made five changes for the second match in succession, with fit-again Alex Whittle back in action at left-back.
Frank Mulhern, Dominic Knowles and Martyn Woolford were also back in action and combined inside three minutes, with the latter firing straight at Cameron Mason when well-placed.
United won their penalty when Mulhern played Woolford through and he was tripped by Mo Ali, with THEWLIS confidently stepping up to send Mason the wrong way from the spot.
Knowles then carved out another opening for Woolford, which he fired narrowly wide.
Peter Crook had to make routine saves to deny Watkinson, Josh Askew and Isaac Sinclair before Brad Abbott, the fifth player to earn a United recall, crashed an effort narrowly wide following Mulhern’s assist.
Knowles teed up Mulhern at the beginning of the second half and he blasted wide from 20 yards.
Crook made a brilliant save to deny Calveley around the hour mark and then tipped Oliver Thornley’s header wide from the resulting corner.
Watkinson was handed his marching orders after leaving an arm in on Warren but the Pilgrims failed to capitalise on their numerical advantage.
Curzon won their own spot-kick which was converted by HALLS following Scott Garner’s foul on Calveley.
Curzon (3-5-2): Cameron Mason; Andrew Halls, Oliver Thornley, Mo Ali; James Baillie (Tunde Bayode 73), George Broadbent, Robbie Evans, Mike Calveley, Josh Askew; Owen Watkinson, Isaac Sinclair (Fabio Tavares 73). Subs (not used): Nicky Wroe, Luke Merrill, Liam Davies.
Boston (4-2-3-1): Peter Crook; Tyrell Warren, Scott Garner, Simon Ainge, Alex Whittle; Brad Abbott, Tom Platt; Martyn Woolford (Jay Rollins 77), Dominic Knowles (Luke Shiels 90), Jordan Thewlis; Frank Mulhern (Jake Wright 73). Subs (not used): Ashley Jackson, Simon Heslop.
Referee: Daniel Locker.
Attendance: 290.