Goals from Mark Jones, Kaine Felix and Scott Garner put the Pilgrims into a 3-0 half-time lead and Zak Mills added a fourth after Jack Kelly had briefly cut the deficit for Forest.
Dennis Greene included Peterborough United striker Jack Friend and fellow trialist Jordan Deacey, formerly of Bradford Park Avenue and AFC Telford United.
Boston (4-4-2): Matt Urwin (Sam Vince 81); Zak Mills, Scott Garner, Carl Piergianni, Liam Marrs; Kaine Felix, Kyle Dixon, Jordan Deacey (Louis Saebe 81), Jamie McGhee (Jay Rollins 46); Mark Jones, Jack Friend (Jack Smith 70).
Referee: Alistair Wilson.
Attendance: 394.