Greece was never threatened in Thursday's Group A match, holding Kazakhstan scoreless for a 14-minute stretch to build a 7-1 lead halfway through the third quarter.
Captain Georgios Afroudakis chipped in with three goals for Greece, while Rustam Ukumanov led Kazakhstan with two.
The win gives Greece three points from three Group A games, boosting its chances of advancing to the quarterfinals. The Greeks still have games against Spain and Australia in the preliminary stage.
Kazakhstan, meanwhile, remains winless in London and sits at the bottom of the group.