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The match required two tie-breaks to separate the pair, but Raonic eventually prevailed 7-6 7-4 6-2.
The first set went by way of serve, before Kubot lost out three times in the tie to give his Canadian opponent first blood.
Both players held serve once more in the second set, and it was Raonic who held his nerve again to take a two-set lead.
The world number nine made lighter work of the final set by capitalising on Kubot's two losses of serve to secure his spot in the next round.