Knowles' crisp 37th minute 25-yarder left Hereford FC keeper Curtis Pond flat-footed at the Jakemans Community Stadium.
The Pilgrims were good value for their victory, but did require a sensational last-gasp save from Cameron Gregory to thwart Jason Cowley.
United played well before the break and forced a succession of corners, with Keziah Martin forcing Pond into his first save in the 33rd minute.
The Pilgrims edged ahead four minutes later when KNOWLES sailed home a beauty from 25 yards which left Pond motionless.
Knowles crashed another effort off target before the break, with Aurio Teixeira repeating the feat at the other end.
Yusifu Ceesay's cross was glanced on to the post by Cowley after the break, before Martin Woods rattled the Hereford crossbar with a 30-yard free-kick.
Kelsey Mooney crashed an effort off target, in between Jai Rowe and Woods both succumbing to injury.
Gregory was called into action at the death with an instinctive stop to thwart Cowley - and preserve United's victory and clean sheet in spectacular fashion.
Boston (4-4-2): Cameron Gregory; Jai Rowe (Dylan Hill 64), Michael Bostwick, Tom Leak, Brad Nicholson; Keaton Ward, Jordan Richards, Martin Woods (Tom Edge 82), Keziah Martin; Kelsey Mooney, Jimmy Knowles. Subs (not used): Ethan Sephton, Oliver Wilson, Tyler Knowles.
Hereford (4-5-1): Curtis Pond; Oliver Southern (Tom Pugh 46), Kyle Howkins, Nathan Cameron, Aaron Skinner; Adam Livingstone, Alex Babos, Lassana Mendes (Ethan Freemantle 67), Aurio Teixeira (Jamie Tolley 81), Yusifu Ceesay; Jason Cowley. Subs (not used): Paul Downing, Adam Rooney.
Referee: Zac Kennard-Kettle.
Attendance: 1,505 (110 visitors).
PIC: Tim Hoff.