Hillary Clinton’s strong debate performance has lifted her standing in a handful of battleground state polls, an indication that her first face-off against Donald J. Trump halted the surge he was enjoying for much of September.

A poll of Florida voters conducted entirely after Monday night’s debate shows Mrs. Clinton receiving the support of 46 percent of likely voters, while Mr. Trump was garnering 42 percent. The survey, conducted by Mason-Dixon polling and research, indicated that Gary Johnson, the Libertarian Party nominee, was the preferred candidate of 7 percent of voters.

Mrs. Clinton’s strength in Florida, a state Mr. Trump almost certainly needs to win if he is to compile 270 electoral votes, owes to her advantage among women and overwhelming support among Hispanics and African-Americans, the poll showed.

A New York Times Upshot/Siena College poll of Florida voters before the debate indicated the race there was effectively tied.