Bayo Akinfenwa was Boston's hero after helping the Third Division strugglers to victory over Swindon in the LDV Vans Trophy.
The 21-year-old recruit, formerly of Barry Town, was on target in the final minute to settle an entertaining tie.
Simon Weatherstone fired narrowly over the bar before Boston went ahead in the 16th minute as Lee Beevers headed home a Mark Angel free kick.
But the Second Division side hauled themselves level on 31 minutes when Steve
Robinson stabbed in after Sebastien Ruster had pulled back a cross from the right.
Both sides then had further openings with Weatherstone and Akinfenwa going close for Boston and Ruster and Jon Stevenson replying for Swindon.
Griemink also pulled off a stunning close-range save to deny Weatherstone 20 minutes from time.
But it was Boston who grabbed the winning goal when Akinfenwa turned the ball in via a post from a Scott Brough cross.
Boston Utd: Bastock, Hogg, Ellender, Hocking, Beevers, Clarke,
Lee Thompson, Bennett, Angel, Akinfenwa, Weatherstone.
Balmer, Jones, Duffield, Croudson, Brough.
Swindon: Griemink, Herring, Viveash, Reeves, Nicholas, Ruster,
Pook, Robinson, Howard, Smith, Stevenson.
Subs: Evans, Duke,
Heywood, Martin, Garrard.
Referee: K Wright (East Anglia).