Jai Rowe and Lewis Padmore had handed visiting Rugby Town a 2-0 National League U19 Alliance lead before Gaukroger replied with a stunning 30-yard free-kick.
Padmore converted a rebound after being denied from the spot by Nick Ivanov before Jenson Newey wrapped up all three points for Rugby, with United's Lewis Bontoft subsequently dismissed in stoppage time.
Boston (3-4-3): Jake Frestle (Nick Ivanov 46); Nathan Stevens, Callum Rodger, Owen Sears; Marshall Young, Mido Turki (Finlay Armond 65), Lewis Bontoft, Jenson Bark (Daniel Fisher 75); Will Jackson, Harrison Holland (Callum Harrison 46), Jamie Gaukroger. Sub (not used): Taylor Gray.