The RAF College Cranwell encounter was settled by 67th and 68th minute goals for the visitors.
The match was otherwise finely-balanced but Gateshead's greater threat in front of goal handed them all three points.
Boston (3-5-2): Andy Hewitt; Todd Devlin, Scott Dawson, Jordan Lote; Niall Delahoy, Lewis Sturman, Jake Beauchamp, Jason Field, Charlie Rossington; Charley Sanders, Jake Platten (Juris Kormis 72).