New York voters have spoken, and Gov. Andrew Cuomo remains the most powerful man in New York politics.

The governor won a resounding victory over the actress and activist Cynthia Nixon in the Democratic primary, protected by a $31 million campaign war chest that helped clear the field of candidates who might have proven more formidable.

His pick for state attorney general, Letitia James, also won big, making it likely his third term will unfold without the inconvenience of someone more independent, like Ms. James’s opponent, Zephyr Teachout, examining his administration.

Yet there were also signs that change was finally knocking on Albany’s door.

Even though it was held, unusually, on a Thursday, more than twice as many people voted in this year’s Democratic primary than did four years ago , a sign of an energized electorate that could pay huge dividends for Democrats in November. If Ms. James wins in November, which is likely, she will become New York’s first black state attorney general and the first black woman to win statewide office.