The Pilgrims were 2-1 victors over National League side FC Halifax Town at The Shay courtesy of headers from Marriott on 15 minutes and Qualter 16 minutes later.
Ex-Pilgrim Dayle Southwell reduced the arrears with a 72nd minute header of his own, but the Pilgrims held on for their second win of pre-season.
Boston (4-4-2): George Willis (Dylan Parkin 63); Ben Middleton (Sam Topliss 63), Ryan Qualter (Trialist J 63), Trialist K (Trialist L 63), Ashley Jackson (Jordan Gough 63); Jonathan Wafula (Nicky Walker 63); Brad Abbott (Grant Roberts 63), Andi Thanoj (Spencer Harris 46), Nathan Arnold; Jonny Margetts (Andre Johnson 63), Adam Marriott.
Referee: Sam Barrott.
Attendance: 371 (26 visitors).
PIC: Darren Murphy (FCHT).