NEW YORK — Nine months after she stepped into the job as a relative unknown, Governor Hochul easily locked up the Democratic party’s nomination for re-election Tuesday, framing up a race against Representative Lee Zeldin, who won the Republican primary.   

Ms. Hochul enters the general election campaign with a big advantage, running as the incumbent with a substantial fundraising lead in a state that has more than twice as many registered Democrats than Republicans and has not had a GOP governor in 16 years.

Ms. Hochul was serving as an under-the-radar lieutenant governor under the shadow of Governor Cuomo until last year, when he resigned amid sexual harassment allegations, catapulting her into office.

Ms. Hochul beat back primary challenges Tuesday from New York City’s elected public advocate, Jumaane Williams, and Representative Thomas Suozzi, a moderate from Long Island. She now turns her eyes to becoming the first woman to win election to the New York governor’s office this fall.

In a nod to the barrier-breaking campaign, Ms. Hochul gave an election night speech Tuesday on a stage underneath a glass ceiling at a Manhattan event space.

“I’m also here because I stand on the shoulders of generations of women, generations of women who constantly had to bang up against that glass ceiling. To the women of New York, this one’s for you,” Ms. Hochul said.

She faces Mr. Zeldin, who is a staunch ally of former President Trump and was among the Republicans in Congress who voted against certifying the 2020 election results.

“Are we ready to fire Kathy Hochul?” Mr. Zeldin said to cheers as he spoke at a victory party on Long Island.

The Long Island congressman will try to become the first Republican elected governor in New York since Governor Pataki was reelected in 2002.

“This November, in the state of New York, one-party rule will end,” he said. “Kathy Hochul will get fired. We will restore balance and common sense to Albany again.”

Ms. Hochul has made bolstering abortion rights a key plank of her campaign. That issue has taken on renewed significance following the Supreme Court’s reversal of Roe v. Wade. 

Ms. Hochul in her Tuesday night speech stressed that the state had “gone on offense to protect abortion rights” and “making the world know that New York State is a safe harbor for America’s women.”

Since taking office in August, Ms. Hochul has sought to step out from Mr. Cuomo’s shadow, promising a clean break from his administration. She has said she was not close to the former governor, who has denied wrongdoing, and was not around to witness any alleged misbehavior.

Still, Mr. Cuomo’s presence loomed over her campaign early on when he began making public appearances this past spring, criticizing Ms. Hochul and Democrats in Albany over their approach to crime and suggesting he might run for his old job. Despite suggesting he might run as an independent, the former governor ultimately did not file to run.

Mr. Zeldin is an Army Reserve lieutenant colonel who has represented eastern Long Island in Congress since 2015.

He defeated primary challenges from a former Westchester County executive, Rob Astorino, businessman Harry Wilson, and the son of Mayor Giuliani, Andrew Giuliani. The former mayor frequently campaigned for his son.

Mr.  Zeldin has focused his campaign on rising crime and criticized Mr. Hochul for not toughening the state’s bail laws, for imposing Covid mitigation mandates and for rising costs. And despite Ms. Hochul seeking to project a fresh start from Mr. Cuomo, Mr. Zeldin has referred repeatedly to the “Cuomo-Hochul Administration.”

“New Yorkers are hitting their breaking point. They’re deciding whether or not to stay here or head to other places,” he said.

He will have to persuade the state’s independent voters, which outnumber Republicans, along with Democrats in order to win the general election. Democrats are expected to focus on Mr. Zeldin’s vocal defense of Mr. Trump during both of his impeachments and objection to the election results. 

Ms. Hochul is also likely to focus on Mr. Zeldin’s statements praising the Supreme Court ruling overturning Roe and his comment that, as governor, he would appoint an anti-abortion state health commissioner.

“We must answer one question,” she said Tuesday night. “Are we going to move New York forward, or let the far-right extremist drag our state backwards?”

Ms. Hochul focused her campaign on steps she took to bolster abortion rights and moves to toughen the state’s gun laws after a racist mass shooting in Buffalo.

Tuesday’s election in New York covered statewide offices and state Assembly races, but primary elections for U.S. House seats and the state Senate will be held August 23. Those elections were delayed because of a redistricting lawsuit that led a court to throw out new political maps.