In the survey, 52 percent of likely voters declared Clinton the winner, while 21 percent said Trump won, and 26 percent said neither one. The online poll of 7,541 people, conducted Sept. 26-27 following the debate, carries an error margin of 1.6 percentage points.
In addition to that lopsided result, Clinton managed to achieve another significant objective by strengthening her base of support. Fully 50 percent of Democrats said the debate had changed their opinion of the former Secretary of State for the better, which could ease her campaign's task in turning out voters on Election Day. Just 2 percent of Democrats said their opinion of Clinton changed for the worse.
Trump did not make compared gains with his base. Just 26 percent of Republicans said the debate changed their opinion of Trump for the better, while 6 percent said it had changed for the worse.
Moreover, Trump lost significant ground among women, a key target group among whom he trails Clinton badly. By 30 percent to 13 percent, female likely voters said their opinion of Mrs. Clinton had improved rather than worsened. By 27 percent to 11 percent, they said their opinion of Trump had worsened rather than improved.
Even more worrisome, 69 percent of female likely voters said Trump lacks the personality and temperament to serve as president. Fully 59 percent said Clinton does have the personality and temperament to serve in the Oval Office.
—By CNBC's John Harwood. Follow him on Twitter: @JohnJHarwood