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Hillary Rodham Clinton is maintaining a steady and commanding lead among the field of Democratic presidential contenders, according to a new national CNN/ORC poll that showed her as the winner of last week’s debate.

Mrs. Clinton, the former secretary of state, leads her rivals with support of 45 percent of registered Democrats. Senator Bernie Sanders of Vermont sits in second place at 29 percent and Vice President Joseph R. Biden Jr., who is contemplating a bid, is in third place with 18 percent.

The survey, which has a margin of error of 5 percentage points, indicates that Mrs. Clinton’s support has solidified after a rough summer in which controversy surrounding her use of a private email server raised questions about her trustworthiness.

However, Mrs. Clinton was seen as the clear winner of the first debate and Democrats said that she was the most qualified to represent the party on major policy issues.

As Democrats await Mr. Biden’s decision, the CNN poll shows they are less eager for him to jump into the race. Just 47 percent said that the vice president should run, down from 53 percent in August.

But Mr. Biden is seen as a stronger opponent against Donald J. Trump, the leading Republican candidate. He tops the billionaire developer by 10 percentage points, while Mrs. Clinton leads him by 5 percentage points in a general election matchup.