Stefanik, whose aggressive questioning of Gay went viral, claimed credit for her exit.

Representative Elise Stefanik of New York, whose questions during a congressional hearing last month put Dr. Claudine Gay and two other prominent university administrators on the spot about antisemitism on their campuses, took a victory lap Tuesday afternoon after Dr. Gay announced her resignation as president of Harvard University.

“TWO DOWN,” Ms. Stefanik crowed on social media, accented by three red siren emojis. Last month, the president of the University of Pennsylvania, M. Elizabeth Magill, resigned just four days after she testified before Congress and evaded Ms. Stefanik’s aggressive line of questioning about whether students who called for the genocide of Jews should be punished.

The contentious exchanges between Ms. Stefanik and all three university presidents came at the tail end of a five-hour congressional hearing called by House Republicans on the rise of antisemitism on college campuses. The moment went viral, forcing the trio of presidents, including Sally Kornbluth of the Massachusetts Institute of Technology, to clarify their responses and leading to a period of intense scrutiny on all three.

In Ms. Gay’s case, that prompted an examination of her past work that fueled plagiarism charges, ultimately causing her to step down on Tuesday.

Ms. Stefanik, the No. 4 Republican in the House, has counted the resignations as a political win.

“I will always deliver results,” Ms. Stefanik, a Harvard alumna, said in a statement on Tuesday. “Claudine Gay’s morally bankrupt answers to my questions made history as the most viewed congressional testimony in the history of the U.S. Congress.” Ms. Stefanik added that “this is just the beginning of what will be the greatest scandal of any college or university in history.”

In an interview with Fox News Tuesday afternoon, Ms. Stefanik promised that an ongoing congressional investigation of the universities that she announced in the wake of the hearing would continue to uncover “institution rot.” And she again claimed credit for Dr. Gay’s resignation, arguing that “this accountability would not have happened were it not for the very clear moral questions at the hearing.”

Those questions almost did not happen. During the hearing, Ms. Stefanik had already tried four times to pin down the trio of administrators. She repeatedly tried and failed to get them to agree with her that calls for “intifada” and use of slogans such as “from the river to the sea” amounted to appeals for genocide against Jews that should not be tolerated on campuses.

They had parried her grilling with lawyerly answers that, on their own, might not have made international headlines. But then they fell into something of a prosecutorial trap laid by Ms. Stefanik, refusing to answer “yes” when she asked whether calling for the genocide of Jews violated their universities’ codes of conduct on bullying and harassment.

“I thought, ‘How can I drill down on this and ask this question in such a way that the answer is an easy ‘yes?’ ”Ms. Stefanik said in an interview last month. “And they blew it.”

Ms. Stefanik, who graduated from Harvard in 2006, has a fraught relationship with her alma mater. After the Jan. 6, 2021, attack at the Capitol, Harvard’s Institute of Politics removed Ms. Stefanik from its advisory board, citing her “public assertions about voter fraud in November’s presidential election that have no basis in evidence.”

Ms. Stefanik, a onetime moderate Republican who more than any other lawmaker in Congress represents to Democrats and anti-Trump Republicans the worst of what happened to the G.O.P. under the sway of Mr. Trump, at the time called her removal “a rite of passage and badge of honor.”

On Tuesday, one of Ms. Stefanik’s top advisers, Garrett Ventry, joked on social media that Ms. Stefanik was now the de facto president of Harvard University.

But she was hardly the only House Republican vying on Tuesday to claim credit for Ms. Gay’s resignation.

Representative John James, Republican of Michigan, shared on social media a clip of his own line of questioning during the hearing and wrote that Dr. Gay’s resignation came “after I questioned her just last month about what actions she’d taken to combat anti Semitism.”