“My opponent, endorsed by him, has run this race very, very close to the Trump handbook, where we call each other names, where we run false advertisements,” he said.

The jabs flew from there, with Mr. DeSantis, calling Mr. Gillum a career politician who distorted the truth about apparently accepting improper gifts from a lobbyist friend and businessmen who were actually undercover F.B.I. agents investigating Tallahassee’s community redevelopment agency. Mr. Gillum insists he is not the target of the investigation, which began in 2015 and has yet to result in any indictments. The gifts, made to Mr. Gillum during a pair of 2016 trips to New York and Costa Rica, are the subject of a separate state ethics investigation.

Records made public on Tuesday suggested that Mr. Gillum knowingly took a free ticket to the hit Broadway musical “Hamilton” from the undercover agents in August 2016. Mr. Gillum maintained in the debate that he did not know the agents had paid for it, though he acknowledged he should have asked to make sure.

“I arrived at the theater and received the ticket from my brother,” Mr. Gillum said “I should have asked more questions to make sure that everything that had transpired was above board.”

Mr. Gillum said he thought his younger brother, Marcus Gillum, had swapped Jay-Z and Beyoncé tickets with Adam Corey, Mr. Gillum’s lobbyist friend, in exchange for the musical tickets. Then, paraphrasing Jay-Z, Mr. Gillum tried to turn the debate to policy issues: “We got 99 issues, and Hamilton ain’t one of them.”

Mr. DeSantis demanded that Mr. Gillum waive confidentiality in the state ethics inquiry, which will not be completed before Election Day. “Get all the evidence and statements out there so the voters of Florida can know everything is on the up-and-up,” he said.

Mr. Gillum countered that Mr. DeSantis should release detailed travel records of more than $145,000 in taxpayer-funded trips he took to New York, including two visits to appear on Fox News, while in Congress. “Where is the evidence of where you went and how our money was spent to be a junket for you to go to New York and hang out in ‘Faux News and Friends’?” he asked.