Reece McMann's 70th minute penalty sealed all three points for the Quakers, who chalked up their first league win of the season in the process.
United's woes were compounded by substitute Mackenzie Burdass' late red card.
Boston (3-4-2-1): Oliver Ford; Bailey Dilley, Owen Sheriff, Taylor Jaine; Krisztian Gagyi, Haydn Tear, Joe Melson, Logan Tate; Han Stevens, Finlay Armond; Sam Harris. Subs (all used): Zane Millar, Mackenzie Burdass, Elliot Foster, Ben Robson, Ben Johnson.
Referee: Michael Brader.
PIC: Russell Dossett