Less than 30 minutes into the first Republican presidential debate, the men onstage were bickering — just as Nikki Haley predicted.

“I think this is exactly why Margaret Thatcher said, ‘If you want something said, ask a man,’” quipped Ms. Haley, the former governor of South Carolina and former ambassador to the United Nations. “If you want something done, ask a woman.”

The response was the beginning of a standout performance for Ms. Haley, who already cut a distinct figure: the lone woman in the Republican field, standing in a white and light blue suit-style dress among a stretch of men in nearly identical red ties.

Her Thatcher line — a favorite on the stump and the inspiration for the title of one of her books — captured the balance she has sought to strike between testing her party’s attitudes and not leaning too far into her gender. But Ms. Haley, who has struggled to gain traction in primary polls dominated by Donald J. Trump, did not always stay above the fray.

She took swings at her rivals and offered a general-election vision for her party that seemed to intrigue some voters and pundits who were impressed with her abilities to speak authoritatively, skillfully break with the pack on some issues and give and take punches.

The showing could inject some much-needed momentum into her campaign. Ms. Haley spent the next morning sitting through a blitz of interviews before she was expected in Chicago for a fund-raiser. At the very least, her allies said, the debate gave a glimpse into why she should not be discounted.

“Nobody thought Nikki Haley could get elected to anything in South Carolina,” said Katon Dawson, a Haley surrogate and the former chairman of the South Carolina Republican Party. And yet, he added, “she has never lost a race.”

Here are four areas where Ms. Haley was able to land a blow and distinguish herself from the field on Wednesday night in Milwaukee.

“Do not make women feel like they have to decide on this issue.”

She went head-to-head with former Vice President Mike Pence on abortion, giving an impassioned defense of women and urging her rivals to stop “demonizing” the issue. As governor of South Carolina, she signed a 20-week ban on the procedure, but on Wednesday, just as she has before, she called for “consensus” on the issue.

“Can’t we all agree that we should ban late-term abortions? Can’t we all agree that we should encourage adoptions? Can’t we all agree that doctors and nurses who don’t believe in abortion shouldn’t have to perform them?” she said, before continuing: “Can’t we all agree that contraception should be available? And can’t we all agree that we are not going to put a woman in jail or give her the death penalty if she gets an abortion?”

Ms. Haley’s attempts to lead her party on a thorny issue haven’t always resonated — partly because, her critics say, she has dodged most questions on the details of her positions. On the stage Wednesday, she broached familiar personal themes, saying she was “unapologetically pro-life” because her husband was adopted and she had trouble conceiving her two children.

But when Mr. Pence sought to establish himself as the staunchest opponent of abortion, telling Ms. Haley that “consensus is the opposite of leadership,” Ms. Haley fired back that he was being dishonest about what was politically possible when it comes to Congress passing a federal ban on abortion.

“When you’re talking about a federal ban, be honest with the American people,” she said, arguing that the 60-vote filibuster threshold in the Senate meant that no Democratic or Republican president would be able to set abortion policy.

The exchange underscored the deep and emotional divide that has emerged among Republicans since the Supreme Court overturned Roe v. Wade last year. Though members of the party largely support that ruling, a fierce electoral backlash to more stringent state-level restrictions has made abortion a politically risky issue for Republicans.

“This guy is a murderer, and you are choosing a murderer over a pro-American country.”

Some of Ms. Haley’s fiercest clashes were with Vivek Ramaswamy, a biotech entrepreneur and political newcomer, over her support for Ukraine in its effort to fight Russia’s invasion, an issue that has starkly divided the field and the party more broadly. She suggested that Mr. Ramaswamy wanted to “hand Ukraine to Russia,” and that President Vladimir V. Putin of Russia had killed Yevgeny V. Prigozhin, the leader of the Wagner mercenary group responsible for a short-lived mutiny.

“This guy is a murderer, and you are choosing a murderer over a pro-American country,” Ms. Haley said to Mr. Ramaswamy, referring to Mr. Putin, whom she also called “thug.” “You don’t do that to friends. What you do instead is you have the backs of your friends.”

Later, she took one of the most memorable shots of the night when she told Mr. Ramaswamy: “You will make America less safe. You have no foreign policy experience and it shows.” This drew loud applause from the audience.

“They all voted to raise the debt, and Donald Trump added $8 trillion to our debt.”

On the campaign trail, Ms. Haley often tells crowds that it is time to put an accountant like herself in the White House. On Wednesday, as her rivals blamed President Biden and Democrats for economic policies that they said had driven up the cost of food and gasoline, Ms. Haley criticized both Republicans and Democrats for increasing the nation’s spending and debt.

“The truth is that Biden didn’t do this to us,” she said. “Our Republicans did this to us when they passed that $2.2 trillion Covid stimulus bill.”

Mr. Biden shared a clip of Ms. Haley in which she said her rivals — Mr. Trump, Mr. Pence, Mr. DeSantis and Senator Tim Scott of South Carolina — had all fueled the national debt increase. “What she said,” the president said on X, formerly known as Twitter.

Economists largely agree that Mr. Biden’s $1.9 trillion pandemic rescue plan in 2021 contributed to the highest inflation rate in decades. But they spread the blame to stimulus passed under Mr. Trump and monetary stimulus by the Federal Reserve, along with disruptions to supply chains caused by Covid-19.

The issues of debt and spending, along with calls for greater transparency in government, were part of Ms. Haley’s stunning come-from-behind-victory in 2010 when she was elected governor. That year, Ms. Haley, the daughter of Indian immigrants, rode the Tea Party wave to become the first woman and first person of color to lead South Carolina — as well as the youngest governor of any state at the time.

“We have to face the fact that Trump is the most disliked politician in America.”

Ms. Haley elicited some boos from the arena audience when she called for “a new generational conservative leader,” pointing out “that-three quarters of Americans don’t want a rematch between Mr. Trump and Mr. Biden.”

“We have to face the fact that Trump is the most disliked politician in America,” she said. “We can’t win an election that way.”

In an interview with the Fox News host Sean Hannity after the debate, Ms. Haley appealed to Republican primary voters to back a candidate other than Mr. Trump, whom she cast as an unsure bet against Mr. Biden.

She said that she believed the criminal indictments against Mr. Trump were politically motivated, but that the cases could nevertheless take him off the campaign trail.

“I served with him, I was proud to serve with him, I agree with him on most issues and he’s my friend,” Ms. Haley said of the former president. “But the reality is we cannot afford Joe Biden.”