BROCKENHURST booked their spot in round four of the FA Vase for the first time in 15 years, defeating Street on penalties.
The Badgers drew 1-1 in Somerset with Christie Ward on target, before progressing 3-2 on spot-kicks after Harry Foster's equaliser.
Substitute trio Mitchell Speechley-Price, Lyle Simpson and Joseph Chamberlain all scored from 12 yards, with goalkeeper James Mayo making a decisive save.
They will host fellow Wessex League outfit New Milton Town in the next round.
New Milton moved into the last 32, also progressing on penalties.
Following a goalless draw at home against Keynsham Town, successful spot-kicks from Ashley Booker, Elliott Pearce-Eavis, Luke Stone and Charles Turner sent the Linnets through 4-2 on spot-kicks.
Bashley exited the competition, losing 2-1 at Bridgwater Town, despite a Harry Bunce strike.
Winning clubs in the fourth round will receive £1,875, with ties due to take place on January 15.
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