United trailed 2-0 at half-time, although they did force themselves back into contention through Miles Lynch after the break.
Solihull scored again before the end to condemn the Pilgrims to defeat in the West Midlands.
Boston (4-3-3): Tom Benton; Daniel Worthington, Charlie Melville (Billy Hodgkiss 60), Josh Spencer, Jordan Sowerby; Miles Lynch, Jacob Pease, Bradley Easey; Steven Dovey (Harry Bunce 60), Karolis Andriulionis, Liam Moran.