The Pilgrims were 2-0 victors over Keighley-based Pro Elite Academy, despite the match finishing goalless after 90 minutes.
Gecas struck in the 95th minute, before wrapping up the victory in the 120th minute, as United successfully navigated their way to round two.
Boston: Sam Buckland, Toby Foreman (Oscar Broom 105), Jack Clayton (Ben Beasley 105), Josh Panton, Daniel Fisk, Kye Rook (Lewis Horne 60), Aron Ealham, Matas Gecas, Freddie Shinn, Denis Matei (Jack Dixon 49), Joe Todd.