LOUDON, N. H.—A decade ago, Kelly Ayotte was narrowly defeated in one of the closest Senate races in the nation. This year, her re-election campaign for governor could serve as a rare bright spot in an otherwise rough year for Republicans.

Ayotte, who was first elected New Hampshire’s governor in 2024, has maintained a steady lead in polls over her Democratic opponent, Cinde Warmington, offering a fresh reminder for Republicans around the nation about how to win over independent-minded voters in battleground states.

In her first term as governor, Ayotte, 58 years old, has emphasized the “New Hampshire advantage”— playing up the state’s low-tax status within New England and quality-of-life benefits—and steered clear of areas where she might end up at odds with the White House.

She has reprised the lighthearted advertising from her 2024 campaign, in which she appeared alongside her husband, Joe Daley, who joked about her snoring and limited cooking skills. In a new ad, Daley tells her, “you’re a great mom,” prompting Ayotte to ask, “And I’ve gotten better at cooking, right?”Daley mouths “no” to the camera and the ad cuts to them eating Chinese takeout.

Republicans are hoping Ayotte at the top of the ticket will boost the party as it tries to maintain control of both chambers of the state legislature and a majority on the state’s executive council while flipping a competitive U.S. Senate seat.

“There’s no question that the Ayotte campaign has got a special sauce that they’ve put together to be very effective in what I think is otherwise going to be a very good year for Democrats around the country,” said Jim Merrill, a longtime Republican strategist in New Hampshire.

Democrats have controlled federal offices in New Hampshire for the past decade, and the state has voted Democratic in every presidential election since 2004. Ayotte, who won her single Senate term in 2010, is the last New Hampshire Republican to serve in the Senate, and Democrats have controlled the two House seats for the past decade.

The state’s Republicans are hoping that Ayotte can help former Sen. John E. Sununu in his Senate battle against Democratic Rep. Chris Pappas. Polls have shown Pappas with a slight lead in the Senate race against Sununu, who is attempting to recapture the seat of retiring Democratic Sen. Jeanne Shaheen.

During an outdoor Oktoberfest festival in Loudon earlier this month sponsored by GOP state Sen. Howard Pearl, Ayotte mingled with local Republicans while a cover band performed Tom Cochrane’s “Life is a Highway,” and Fleetwood Mac’s “Dreams” and guests sampled beer and nibbled on hamburgers and hot dogs.

“[Ayotte’s] a great top of the ticket for us here, and hopefully that transcends down ticket and helps us in some of those races that are a little closer,” Pearl said. “She’s been an independent thinker…I think Granite Staters, they’ve always voted more for the individual than perhaps maybe a party line.”A recent AARP poll offered a window into the potential for ticket-splitting among the state and federal races. In the race for governor, the poll found Ayotte at 52% and Warmington at 45%, with 3% undecided. In the Senate race, Pappas had an edge with 51% and Sununu at 44%, with 5% undecided.

Despite the ticket-splitting, some Republicans said Ayotte’s popularity could ultimately help Sununu win. Others expressed reservations that she would boost Sununu or other down-ballot candidates. “She’s going to benefit from that, but I don’t think there’s going to be another Republican who’s going to benefit from ticket splitting,” said Fergus Cullen, former chairman of the New Hampshire Republican State Committee. Ayotte’s office didn’t respond to a request for an interview.

Warmington, who previously served on the executive council, the five-member elected board that shares power with the governor, has called Ayotte an “absentee governor” on issues such as housing, education funding, child care costs and “standing up to Donald Trump.”

Warmington said New Hampshire residents “see the damage that she’s doing—the skyrocketing cost of housing and the fact that she’s jacked up the cost of health care…they’ve had it and there’s a real choice in this election.”Republicans have made Warmington’s past lobbying for Purdue Pharma, the maker of OxyContin, a centerpiece of their attacks in the state, which has been hard hit by the opioid crisis.

Warmington, who lobbied for the company in 2001-2002, has defended her work, noting she was fighting for patients to get access to healthcare. She has faulted Ayotte for not pursuing litigation against Purdue Pharma as the state’s attorney general.

Ayotte became the state’s first woman to serve as attorney general in 2004 when she was appointed by Republican Gov. Craig Benson and confirmed by the executive council. When Republican Sen. Judd Gregg announced his retirement, Ayotte campaigned for the Senate, narrowly defeating Tea Party-backed lawyer Ovide Lamontagne in the 2010 GOP primary, then easily dispatching Democratic Rep. Paul Hodes in the general election.

Ayotte’s political ascension stalled in 2016 when she was defeated for re-election by then-Gov. Maggie Hassan by roughly 1,000 votes. Just a month before that election, Ayotte pulled her endorsement of Trump when the “Access Hollywood” tape emerged of Trump talking in crude sexual terms about women in 2005. While Ayotte narrowly lost, Republican Chris Sununu won his governor’s bid.

Sununu, the younger brother of the party’s Senate nominee this year, condemned Trump’s remarks but still backed him as the Republican presidential nominee.

Republicans in the state credit Ayotte with how she has managed to navigate national party dynamics with Trump in power. One example of her balancing act came earlier this year as she responded to a proposed U.S. Immigration and Customs Enforcement detention center in Merrimack, which prompted public outcry in the town after it was reported about in late December. In late January, Ayotte said she told officials at the Department of Homeland Security and White House that Merrimack should be consulted about the proposed plans. In late February, after meeting with then-DHS Secretary Kristi Noem, Ayotte announced DHS wouldn’t move forward with the proposed facility.

On the campaign trail, in ads and on social media, Ayotte has largely focused on issues specific to New Hampshire. In one ad, she touts the state’s school cellphone ban. In the one with her husband, Joe, she talks about her work to increase housing construction and press utility companies to lower bills.

“She’s done a really good job of being Kelly from New Hampshire,” Merrill said.

Write to Ken Thomas at ken.thomas@wsj.com and Sabrina Rodriguez at sabrina.rodriguez@wsj.com