Alex Wiles’ strike had the Seadogs in front at half-time and an Aidan Rutledge double sandwiched a Deji Sotona reply from the penalty spot after the break.
Brad Nicholson crashed home a stoppage time free-kick, but it was too little, too late for the Pilgrims.
The match was delayed until 8.15pm as home officials worked hard to make the surrounding areas safe for public use following the rapid onset of freezing temperatures.
The Pilgrims created the best early chances with goalkeeper Ryan Whitley denying Jimmy Knowles and Sotona.
Boro took the lead when WILES lashed an effort into the top corner after Michael Bostwick had only partially cleared a Dominic McHale cross from the right.
Gateshead loanee RUTLEDGE doubled the advantage seven minutes after the break with a fine, driven finish from outside the box.
United were handed a lifeline when their former loanee Whitley dropped a routine ball and hauled down SOTONA as he attempted to make amends - with the Doncaster Rovers loanee powering home the spot-kick.
However, United’s respite was shortlived qnd RUTLEDGE bobbled home his second of the game in the 66th minute following a lucky bounce off Aaron Chapman.
United kept fighting and reduced the arrears when NICHOLSON arrowed home a brilliant 25-yard set-piece after the marauding Sotona had once again been upended.
Scarborough (4-2-3-1): Ryan Whitley; Alex Brown, Bailey Gooda, Will Thornton, Luca Colville; Alex Purver, Alex Wiles (Lewis Maloney 88); Dominic McHale (Curtis Durose 86), Ollie Dyson, Harry Green (Dom Tear 70); Aidan Rutledge. Sub (not used): Joe Cracknell (gk).
Boston (4-4-2): Aaron Chapman; Jai Rowe, Michael Bostwick, Tom Leak, Brad Nicholson; Sam Smart (Keaton Ward 60), Jordan Richards, Keziah Martin, Deji Sotona; Jimmy Knowles (Kelsey Mooney 60), Jacob Hazel (Michael Gyasi 76). Subs (not used): Martin Woods, Zak Mills.
Referee: Gareth Thomas.
Attendance: 1,226 (71 visitors).
PIC: Lee Keuneke.