Limb, playing his first youth team match since before Christmas, swooped to score the winner in the 90th minute to hand the Pilgrims all three points at Boston Town’s DWB Stadium.
The result consolidated United’s position in fourth place of the Football Conference Youth Alliance.
Boston (4-1-2-1-2): Travis Portas; James Gordon, Harry Bunce, Bailey Forth, Peter Evison (Kofi Ross 55); Jack Dykes; George Hobbins (Harry Vince 55), Oli Drummond; Tinashe Chavundura; Harry Limb, Louis Saebe. Subs (not used): Liam Mead, Harry Payne (gk).