The Russian five-times Grand Slam champion, out since January with a right shoulder injury that required surgery, saved a couple of set points in a tight opening set in blazing sunshine but romped through the second in quick time.
It was Sharapova's first competitive match since she withdrew from the St Petersburg Open in January, saying she needed to sort out the problem with her serving shoulder.
Apart from some double-faults in the opening set when she dropped serve to trail 5-6, there was nothing to suggest the 32-year-old was having any lingering problems from the right shoulder that has caused her problems for a decade.
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She broke back immediately to force a tiebreak but had to fend off a set point at 6-7 and another at 7-8 as the 21-year-old Kuzmova, ranked 39 places higher than Sharapova at 46, troubled the Russian with some big serves.
Sharapova, who took a wildcard for the tournament, snatched the opener on her second set point as Kuzmova netted a forehand.
There was little resistance from Kuzmova in the second set as Sharapova set up a potential clash with top seed and reigning Wimbledon champion Angelique Kerber.
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