Former Vice President Joseph R. Biden holds an 11-point lead over Sen. Elizabeth Warren in the race for the 2020 Democratic presidential nomination, according to a poll released Tuesday that showed Ms. Warren and Sen. Bernard Sanders inch closer to the front-runner after last week’s debates.

Mr. Biden was the top choice of 32% of Democrats and Democratic-leaning independents, followed by Ms. Warren at 21% and Mr. Sanders at 14%, according to the Quinnipiac University poll.

They were followed by Sen. Kamala Harris at 7% and Pete Buttigieg, mayor of South Bend, Indiana, at 5%.

“Biden survives, Warren thrives and Harris dives as debate number two shakes up the primary,” said Tim Malloy, assistant director of the Quinnipiac University Poll.

A July 29 Quinnipiac poll had Mr. Biden in the lead with 34% support, followed by Ms. Warren at 15%, Ms. Harris at 12% and Mr. Sanders at 11%.

“Sen. Elizabeth Warren’s policy heavy presentation and former Vice President Joseph Biden’s ability to handle the heat from all corners put them on top,” Mr. Malloy said. “Sen. Kamala Harris, whose 20 percent score put her neck-and-neck with Biden in a Quinnipiac University poll July 2 after the first debate, is now a distant fourth with 7 percent.”

Close to half of respondents — 49% — said Mr. Biden has the best chance of beating President Trump. Mr. Sanders was at 12%, followed by Ms. Warren at 9% and Ms. Harris at 6%.

But 32% said Ms. Warren has the best policy ideas, followed by Mr. Biden at 17%, Mr. Sanders at 16%, and Ms. Harris and Mr. Buttigieg at 5% apiece.

Of those who said they tuned into most or all of last week’s debates or tracked subsequent coverage, 28% said Ms. Warren did the best job. She was followed by Mr. Biden at 15%, Mr. Sanders and Ms. Harris at 8% apiece, and Sen. Cory Booker at 7%.

Of that group, Mr. Biden and self-help expert Marianne Williamson led the way on who respondents thought did the worst job at the debates, at 9% each. Ms. Harris was next at 7%, followed by New York Mayor Bill de Blasio and former Rep. John Delaney at 6% each.

The overall survey of 807 Democrats and Democratic-leaning independents was conducted from Aug. 1-5 and has a margin of error of plus or minus 4.1 percentage points.

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