While they aren’t exactly running as a ticket, there is widespread agreement among Florida political pros that Democratic Sen. Bill Nelson is benefiting from his party’s gubernatorial candidate, Tallahassee Mayor Andrew Gillum.

Mr. Gillum, a leftist in the mold of Sen. Bernard Sanders of Vermont, won an unexpected victory in the Democratic primary for Florida governor. As a young black face on the scene, he is expected to generate more enthusiasm and votes in November, which could help Mr. Nelson in his tight re-election bid against Republican Gov. Rick Scott.

“Florida’s gubernatorial and U.S. Senate contests are practically glued together,” said Susan MacManus, a political scientist and the dean of the Sunshine State’s political analysts. “In fact, many believe the governor’s race will be the turnout driver rather than the Senate race.”

Mr. Nelson is embracing the ticket approach. He stopped by an Orlando rally Saturday for Mr. Gillum and his formal running mate, lieutenant governor hopeful Chris King.

Mr. Scott’s campaign, meanwhile, said he doesn’t have any joint appearances scheduled with his party’s gubernatorial candidate, former Rep. Ron DeSantis.

Both the senatorial and governor’s races are close, according to the Real Clear Politics average of polls, which gives Mr. Gillum a 3-point lead in the governor’s race and Mr. Scott a 1.6-point lead for the Senate.

But among black voters. Mr. Gillum holds a commanding 93 percent to 2 percent advantage over Mr. DeSantis, according to a recent Quinnipiac University survey.

“Gillum helps Nelson because he inspires a different base,” Democratic consultant Steve Vancore said. “Younger, millennial, Bernie/progressive voters really love Gillum and were supportive but not enthusiastically so for Sen. Nelson.”

In other words, should the black vote turn out for Mr. Gillum, that could spell trouble for Mr. Scott.

“The governor’s race is going to have some influence over the Senate,” said Rick Wilson, a Republican strategist in Florida and prominent “Never Trumper.” “Andrew Gillum will activate the African-American vote, perhaps substantially.”

Carol Weissert, a political science professor at Florida State, said the “question should make for a fun two months.”

“The truth is Bill Nelson is not a very exciting candidate,” Ms. Weissert said. “Will the base turn out for him? Andrew Gillum changes that calculus.”

Florida isn’t the only state where a governor’s race will affect the Senate battle. In Texas, Republican Gov. Greg Abbott’s massive campaign fund is likely to help turn out voters who could also assist Republican Sen. Ted Cruz.

Nevada, Arizona, Tennessee and Wisconsin are among other states where governor’s races and Senate races could play off each other.

In Florida, the Scott camp hopes to use the ticket-style relationship to its advantage by trying to tie Mr. Nelson to Mr. Gillum’s left-wing stances.

The mayor supports a platform backed by the Democratic Party’s surging progressive base that includes abolishing U.S. Immigrations and Customs Enforcement, raising the minimum wage to $15 an hour, government-backed “Medicare for all” health care, and free public college tuition.

Reflecting the concerns of some traditional Democrats that the far-left positions could hurt with independent voters, Mr. Nelson has shown uncertainty about how much he agrees with Mr. Gillum’s positions. Mr. Nelson initially called the mayor’s ideas “mainstream,” but he has since said he does not want to abolish ICE and would raise the hourly minimum wage to $12.

“It seems like Bill Nelson is stuck between a rock and a hard place,” Republican National Committee spokeswoman Taryn Fenske said. “He needs the votes of Democrats and independents to continue his job as a career politician but is uncomfortable fully embracing the out-of-touch policies that Andrew Gillum is advocating.”

The contests in Florida are being closely watched not only because the Democrats’ dream of seizing a Senate majority would take a big hit if Mr. Nelson is defeated, but also because the matchup between Mr. Gillum and Mr. DeSantis is viewed as something of a showdown between Trump Republicans and Sanders Democrats two years before the next presidential election.

Mr. Nelson and Mr. Gillum already have done what they can to make the races a referendum on President Trump, who has enthusiastically endorsed Mr. Scott and Mr. DeSantis.

In return, Mr. Scott’s campaign has made much of Mr. Nelson’s reluctance to say how he will vote on Supreme Court nominee Brett M. Kavanaugh, whom a majority of Floridians support. Instead, Mr. Nelson tells supporters he is working to keep Mr. Trump from flooding the federal bench with “extremist” or “far right” judges.

Although the Quinnipiac poll showed a majority of Floridians “say Trump is not an important factor in the governor’s race,” the Gillum campaign has been quick to respond to tweets and what it calls provocations from Mr. Trump.

“You have a great candidate in Florida. It’s called the Republican candidate: Ron DeSantis,” Mr. Trump tweeted last weekend. “Ron for governor. This election is a choice between Democrats who want to abolish ICE and Republicans who want to abolish MS-13. It’s very simple.”

After Mr. Trump took a swipe at the left-wing positions in vogue with some Democrats, Mr. Gillum responded on Twitter, “Mr. President, my name is Andrew Gillum and I’m going to be the next Governor of Florida because lies and scare tactics don’t vote, people do.”

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