BIRMINGHAM, Alabama — Doug Jones, a Democratic former prosecutor who mounted a seemingly quixotic Senate campaign in the face of Republican dominance here, defeated his scandal-scarred opponent, Roy Moore, after a brutal campaign marked by accusations of sexual abuse and child molestation against the Republican, according to The Associated Press.

The upset delivered an unimagined victory for Democrats and shaved Republicans’ unstable Senate majority to a single seat.

Jones’ victory could have significant consequences on the national level, snarling Republicans’ legislative agenda in Washington and opening, for the first time, a realistic but still difficult path for Democrats to capture the Senate next year. It amounted to a stinging snub of President Donald Trump, who broke with much of his party and fully embraced Moore’s candidacy, seeking to rally support for him in the closing days of the campaign.

Amid thunderous applause from his supporters at a downtown hotel, Jones held up his victory as a message to Washington from voters fed up with political warfare. For once, he said, Alabama had declined to take “the wrong fork” at a political crossroads.

“We have shown the country the way that we can be unified,” Jones declared, draping his election in the language of reconciliation and consensus. “This entire race has been about dignity and respect. This campaign has been about the rule of law.”

Trump tweeted his congratulations to Jones “on a hard fought victory.”

“The people of Alabama are great, and the Republicans will have another shot at this seat in a very short period of time,” he wrote. “It never ends!”

Propelled by a backlash against Moore, an intensely polarising former judge who was accused of sexually assaulting young girls, Jones overcame the state’s daunting demographics and deep cultural conservatism. His campaign targeted African-American voters with a sprawling, muscular turnout operation and appealed to educated white voters to turn their backs on the Republican Party.

Those pleas paid off Tuesday, as precincts in Birmingham and its suburbs handed Jones overwhelming margins while he also won convincingly in Huntsville and other urban centres. The abandonment of Moore by affluent white voters, along with strong support from black voters, proved decisive, allowing Jones to transcend Alabama’s rigid racial polarisation and assemble a winning coalition. And solidifying Jones’ victory were the Republican-leaning residents who chose to write in the name of a third candidate rather than back one of the two major party nominees. More than 20,000 voters here cast write-in ballots, which amounted to 1.7 percent of the electorate — about the same as Jones’ overall margin.

To progressive voters, Jones’ victory was a long-awaited rejection of the divisive brand of politics that Alabama has inevitably rewarded even as some of its Southern neighbours were turning to more moderate leaders.

At a party for Jones, Sue Bell Cobb, a former chief judge of the Alabama Supreme Court, said he had overcome a culture of “toxic partisanship,” reaching out to Republicans and electrifying restive Democrats.

“Never has there been this level of civic engagement,” said Cobb, who is planning to run for governor next year. “Never has it happened.”

She was drowned out by a raucous cry from her fellow Democrats and clasped her hands to her face as she saw on a huge projection screen that Jones had pulled ahead. Mayor Randall Woodfin of Birmingham, a newly inaugurated Democrat standing just feet away, beamed as returns from his city helped put Jones over the top.

“It feels great,” he said with undisguised elation. “It sends a message not just to America but to the world.”

The campaign, originally envisioned as a pro forma affair to fill the Senate seat left vacant by Jeff Sessions, now the attorney general, developed in its final months into a referendum on Alabama’s identity, Trump’s political influence and the willingness of hard-right voters to tolerate a candidate accused of preying on teenage girls.

Jones, 63, best known for prosecuting two Ku Klux Klansmen responsible for bombing Birmingham’s 16th Street Baptist Church in 1963, offered himself chiefly as a figure of conciliation. He vowed to pursue traditional Democratic policy aims, in areas such as education and health care, but also pledged to cross party lines in Washington and partner with Sen. Richard C. Shelby, the long-tenured Alabama Republican, to defend the state’s interests.

Moore did little in the general election to make himself more acceptable to conventional Republicans. To the extent he delivered a campaign message, it was a rudimentary one, showcasing his support for Trump and highlighting Jones’ party affiliation. But after facing allegations in early November that he sexually abused a 14-year-old girl and pursued relationships with other teenagers, Moore became a scarce presence on the campaign trail.

On election night, as the results came in from Alabama’s cities and Moore’s lead evaporated, the mood at the candidate’s election night party in Montgomery darkened. A saxophonist played a slow rendition of “Amazing Grace,” and the crowd quieted as the results from The New York Times website posted on a projection screen turned toward Jones.

Taking the stage over an hour after The Associated Press called the race, Moore refused to concede and instructed a subdued crowd to “wait on God and let this process play out.”

“Go home and sleep on it,” he told supporters.

The election is a painful setback for Republicans in Washington, who have already struggled to enact policies of any scale and now face even tougher legislative math. Moore’s success in the Republican primary here, and the subsequent general-election fiasco, may deter mainstream Republicans from seeking office in 2018 and could prompt entrenched incumbents to consider retirement.

But there is also a measure of relief for some party leaders that Moore will not join the chamber, carrying with him a radioactive cloud of scandal. A number of Republicans, including Sen. Mitch McConnell of Kentucky, the majority leader, had indicated that Moore would face an ethics investigation if he were elected and possibly expulsion from the Senate.

Trump and Republican activists would most likely have opposed such a measure, setting up a potentially drastic, monthslong clash within the Republican Party, now averted thanks to Jones.

Still, that relief comes at a steep price. Before the election in Alabama, Republicans were heavily favoured to keep control of the Senate in 2018, when Democrats must defend 25 seats, including 10 in states that Trump carried in 2016. Just two or three Republican-held seats appear vulnerable, in Arizona, Nevada and Tennessee.

But after Jones is sworn in, Republicans will control only 51 seats, creating a plausible route for Democrats to take over.

Alexander Burns and Jonathan Martin/The New York Times