Brad Nicholson's header seven minutes before half-time sealed United's safe passage at the expense of their newly-promoted visitors.
United, led by the excellent Michael Bostwick, repelled plenty of Rushall pressure after the break, although keeper Cameron Gregory was not forced into a meaningful save.
The Pilgrims started brightly on the 3G surface - in the first-ever meeting between the sides.
Jimmy Knowles had a header saved by Jake Weaver early on, following Kelsey Mooney's cross from the left.
United edged ahead seven minutes before the break when NICHOLSON got up highest at the back post to bullet a header low past Weaver, following Keaton Ward's corner delivery.
The Pilgrims almost repeated the feat on the stroke of half-time when Mooney glanced just wide on the end of another Ward flag-kick.
Weaver produced an excellent save after the break to deny Ward from 25 yards, while Gregory fielded a tame effort from Sam Mantom.
Andre Carvalho-Landell had an effort ruled out for offside, before skying another effort from inside the penalty area, while terrific defending from the Pics' Jordaan Brown denied Jimmy Knowles with four minutes to play.
Rushall (3-4-2-1): Jake Weaver; Kristian Green, Sam Whittall, Jordaan Brown; Jourdain Masidi (Callum Coyle 75), Alex Fletcher, Tom Tonks (Will Shorrock 76), Ronan Maher; Sam Mantom, Jake Gosling (Danny Waldron 84); Andre Carvalho-Landell. Subs (not used): Lewis Hudson, Alex Moore, Mitchell Clarke, Daniel Cooper (gk).
Boston (4-4-2): Cameron Gregory; Tyler Knowles (Keziah Martin 63), Michael Bostwick, Brad Nicholson, Dylan Hill; Keaton Ward, Jordan Richards, Martin Woods, Finley Thorndike (Michael Gyasi 72); Kelsey Mooney, Jimmy Knowles. Subs (not used): Ethan Sephton, Sam McLintock, Sam Essien, Oliver Wilson, Jake Lovelace (gk).
Referee: Darren Rogers.
Attendance: 434.
PIC: Chris Bray.