The reigning world champions currently lie third in Group A with one match to play, but they now know they will qualify.
Kazakhstan - with four defeats in four - have no chance of getting through to the next round. Despite going behind in the opening quarter, Italy went on to win the period 4-2.
They extended their lead by winning the second quarter by the same scoreline, taking the teams into the half-time break at 8-4.
The Kazakh team fought back well in the second half, holding Italy to a 1-1 draw in the third period, and scoring the only goal of the fourth, leaving the final score 9-6 to Italy.
Pietro Figlioli, Valentino Gallo, Christian Presciutti and Danijel Premus each scored a brace for the Italians, while Amaurys Perez netted one.
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