The Kazakhs sunk to their third successive defeat of the Games, while the 11-4 victory was the Greek side's second win out of three Group A matches.
Greece took a 2-1 lead in the first quarter after going ahead in the third minute.
Indiscipline from Kazakhstan allowed their opponents to score twice from man-up situations as the Greeks netted four unanswered goals in the second quarter to take a 6-1 lead into the half-time break.
The margin was extended in the third quarter, with Greece scoring three more to Kazakhstan's one.
A stronger finish from the Kazakhs allowed them to share the spoils in the fourth, but Greece cruised home to seal a comfortable victory.
Five goals from Ioannis Fountoulis and three from captain Georgios Afroudakis put Greece in a dominant position, while single strikes from Konstantinos Kokkinakis, Evagelos Delakas and Konstantinos Mourikis beefed up the tally.
The Kazakh goals came from Vladimir Ushakov, Sergey Gorovoy and Rustam Ukumanov, who fired in two.