The Pilgrims fell behind inside two minutes through Ciaran McGuckin - but levelled six minutes later through Luke Shiels' first goal of the season.
McGuckin put the Seadogs back in front a minute before half-time, only for substitute Wright to grab a timely leveller with 11 minutes left to play.
United boss Ian Culverhouse had opted to make six changes to the side which drew 2-2 against Gloucester City last time out on January 7, with Tiernan Brooks, Ethan Septhon and Lirak Hasani all handed debuts.
Brooks' first task was to pick the ball out of the back of the net when McGUCKIN got on the end of Luca Colville's corner after just 66 seconds.
United responded positively though and SHIELS sailed home his own header from a Billy Chadwick corner delivery in the eighth minute.
The Pilgrims were behind at half-time with Sam McLintock carelessly giving possession away inside his own penalty area and McGUCKIN arrowing home his second of the game.
Tre Mitford was presented with a glorious chance to equalise after the break - but he headed straight at Joe Cracknell from a Zak Mills cross from the right.
Brooks made a crucial intervention to touch Alex Wiles' low drive on to the post before saving well at the other post to deny Michael Coulson - either side of United's equaliser in the 79th minute, with WRIGHT blasting home Zak Goodson's cross from the right.
Boston (4-1-2-1-2): Tiernan Brooks; Zak Mills, Luke Shiels, Jo Cummings (Jordan Burrow 63), Ethan Sephton; Tom Platt; Lirak Hasani (Scott Pollock 68), Sam McLintock; Billy Chadwick (Jake Wright 63); Tre Mitford, Zak Goodson. Subs (not used): Ben Pollock, Luther Munakandafa.
Scarborough (4-3-3): Joe Cracknell; Ryan Watson, Kieran Weledji, Bailey Gooda, Kieran Burton; Alex Wiles (Emmanuel Ilesanmi 83), Lewis Maloney, Kieran Glynn (Simon Heslop 74); Luca Colville, Michael Coulson, Ciaran McGuckin (Ashley Jackson 64). Subs (not used): Danny Greenfield, Matt Bancroft (gk).
Referee: Dale Baines.
Attendance: 1,726 (183 visitors).
PIC: Nikolay Hristov.