The Pilgrims prevailed 3-1 at Worksop Town, having led 2-0 at half-time courtesy of Trailist F's sixth minute opener and Green's 16th minute penalty.
Thewlis added United's third with eight minutes to play after Steve McDonnell had halved the arrears for Worksop in the 69th minute.
Boston (4-2-3-1): George Willis (Peter Crook 65); Karl Byrne, Trialist D (Ben Middleton 76), Trialist C (Luke Shiels 65), Alex Whittle; Trialist B (Tom Platt 76), Andi Thanoj (Brad Abbott 46); Trialist E (Jay Rollins 46), George Green (Jordan Thewlis 72), Jonathan Wafula (Tom Clare 65); Trialist F (Ashley Jackson 76).
Referee: Anthony Tankard.
Attendance: 287.