Karen Handel, a veteran Republican officeholder, overcame a deluge of liberal money to win a special House election in Georgia on Tuesday, bridging the divide in her party between admirers of President Trump and those made uneasy by his turbulent new administration.

Ms. Handel, 55, fended off Jon Ossoff, a 30-year-old Democrat and political newcomer who emerged from obscurity to raise $25 million from progressives across the country eager to express their anger at Mr. Trump. That fervor quickly elevated what would otherwise have been a sleepy local race into a high-stakes referendum on Mr. Trump and the most expensive House campaign in history.

The surprisingly easy victory for Ms. Handel, a former Georgia secretary of state and Fulton County official, averted a humiliating upset for Republicans in an affluent, suburban Atlanta district — Georgia’s Sixth — that they have controlled for nearly 40 years. And it showed that Republicans skeptical of Mr. Trump remained comfortable supporting more conventional candidates from their party.

The apparent success of relentless Republican attacks linking Mr. Ossoff to the House minority leader, Nancy Pelosi, and her “San Francisco values” also affirmed the efficacy of tying Democratic candidates in conservative districts to their brethren in more liberal parts of the country.

With all 208 precincts reporting, Ms. Handel had 51.9 percent of the vote to Mr. Ossoff’s 48.1 percent.

Addressing supporters in Atlanta, Ms. Handel noted with pride that she had become the first Republican woman sent to Congress from Georgia, and she pledged to represent all of her constituents, including Mr. Ossoff’s supporters. But she made clear that she would work to pass major elements of the Republican agenda, including health care and tax overhauls.

“We have a lot work to do,” Ms. Handel said. “A lot of problems we need to solve.”

For Democrats, the loss was demoralizing after questionable “moral victories” in two earlier special election defeats, for House seats in conservative districts in Kansas and Montana. Mr. Ossoff appeared so close to victory that Democrats were allowing themselves to imagine a win that would spur a wave of Republican retirements, a recruitment bonanza and a Democratic fund-raising windfall heading into the 2018 midterm elections.

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