The Pilgrims accounted for Norwich City RDP at Freiston FC courtesy of Bontoft's brace either side of the break.
He opened the scoring with a rising finish in first half stoppage time before glancing home Jamie Gaukroger's free-kick delivery in the 57th minute.
Boston (4-3-3): Nick Ivanov; Jamie Gaukroger, Harry Cranfield, Daniel Fisher, Nathan Stevens; Lewis Bontoft, Marshall Young, Mido Turki (Marc Tucker 60); Xander Crashley, Harrison Holland (Cole Willerton 69), Jenson Bark.