Within an hour of Alexandria Ocasio-Cortez’s stunning upset of a fellow Democratic stalwart, Representative Joseph Crowley of Queens, staffers for Mr. Cuomo were contacting reporters calling her victory an anomaly borne out of the minority-majority demographics in the district. The reason for such spin was clear: Mr. Cuomo, 60, is facing a primary challenge of his own, from the actress Cynthia Nixon, who, like Ms. Ocasio-Cortez, is running for office for the first time. The two women had endorsed each other, and Ms. Nixon was reveling in her fellow upstart’s unexpected victory, calling it a win “for progressive Democrats over corporate Democrats.”