Newsham gave United a 19th minute lead which was doubled by a stunning Miller strike on 34 minutes and Milnes virtually wrapped up the victory with a well-taken third three minutes after the break following slick interchange with Newsham and Ian Ross from a quick free-kick.
Stags' substitute Ben Hutchinson added a consolation for the visitors on 76 minutes for a side boasting considerable first team experience, but United stood firm to claim a deserved win.
Boston (3-5-2): Ashley Timms; Conor Marshall, Scott Garner, Carl Piergianni; Peter Bore (Charley Sanders 85), Ian Ross (Spencer Weir-Daley 54), Indy Aujla (Ben Fairclough 75), Ben Milnes, Netan Sansara; Marc Newsham, Ricky Miller (Elliott Green 75). Subs (not used): Jordan Nuttell, Billy Bennett, Sam Vince (gk).
Referee: Declan Ford