Democrat Bill Nelson concedes after a bitterly contested election that had two recounts.

Republicans shored up their U.S. Senate majority on Sunday when Florida Gov. Rick Scott narrowly prevailed over Democratic Sen. Bill Nelson, who conceded defeat nearly two weeks after Election Day as a second recount left him trailing by about 10,000 votes. Mr. Scott’s pickup of a Democratic-held seat gives the GOP a 52-to-47 edge in the Senate, with one seat still to be decided by a runoff election in Mississippi this month that the Republican is favored to win. That would give the GOP a net gain of two seats in the Senate for the new Congress as Democrats have widened their advantage in the House in recent days—amplifying the split nature of the next Congress that will convene in January. Over the weekend, Democrats completed their sweep of Southern California’s longtime conservative bastion of Orange County, putting their House majority at 232 to 198, for a net gain of 37 seats, with five races still uncalled.

Mr. Scott’s win over the 76-year-old three-term senator is his third nail-biting statewide victory, after two close elections for governor. For the first time in more than a century, Florida will be represented in Washington by two GOP senators. Republicans cheered the result. “This was the third time Rick Scott’s been written off as a likely loser,” said state Sen. Joe Gruters, who was co-chairman of Mr. Trump’s 2016 campaign in Florida. “I think Bill Nelson’s age caught up with him in terms of the rigors of a campaign. You didn’t see him out there. Rick Scott was like the Energizer Bunny.”

The victory marked the second major Florida win for Republicans in recent days. Democrat Andrew Gillum, who ran to succeed Mr. Scott as governor, conceded to his GOP opponent, Rep. Ron DeSantis, less than 24 hours before Mr. Nelson’s Sunday concession. Heading into the 2020 presidential election, the one-two punch of those defeats were a sobering setback for Democrats, who had hoped to regain footing in a state Mr. Trump won in 2016 but that President Obama had won twice. “We’re not in any kind of position of strength here in Florida,” said Alex Sink, the 2010 Democratic gubernatorial nominee who lost to Mr. Scott by 1 percentage point. Ms. Sink said she worries 2020 presidential candidates may not see the state as competitive and focus on other, less expensive battlegrounds such as Arizona and Ohio. Martha Barnett, a veteran Democrat in Tallahassee, the state capital, said that grassroots enthusiasm shown for Mr. Gillum, who ran as an unabashed progressive, showed Florida is moving in a different direction. “I think 2020 and 2024 are going to be very different elections. I’m just sorry we don’t have Bill Nelson as the leader of our party,” Ms. Barnett said.

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