The Dons locked the ball in their forward 50 for the first three minutes of the term, before a Mitch Brown snap brought the margin back to two points.
Jonathan Patton steadied for the Giants after a high tackle on Anthony McDonald-Tipungwuti was overlooked.
GWS stepped up the pressure, laying 11 tackles to four in the first ten minutes of the quarter to take a 19 point lead.
A Joe Daniher goal from outside 50 gave the Bombers a chance with 8:25 remaining.
But Toby Greene dribbled one through to secure the win for the Giants.
David Zaharakis (25), Brendon Goddard (24) and Adam Cooney (24) were the major ball winners for the Dons, while Orazio Fantasia kicked four goals.