A majority believe Hillary ClintonHillary Diane Rodham ClintonGOP senator says idea that Ukraine interfered in US election is 'not a conspiracy theory' Cotton: Democrats are 'upset that their witnesses haven't said what they want them to say' Trump's troubles won't end with a Senate acquittal MORE won her party's first debate on Tuesday, but the Democratic front-runner received just a small bump in a poll from the perceived victory.

Fifty-six percent of Democrats and Democratic-leaning independents saw Clinton as the winner, compared to 33 percent who thought Sen. Bernie SandersBernie SandersPoll: Sanders leads Biden by 9 points in Iowa Poll: Biden leads in Iowa ahead of caucuses The Memo: Impeachment dominates final Iowa sprint MORE (I-Vt.) won, according to the NBC News/Survey Monkey survey released on Friday.

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Only 3 percent, it added, believe the former secretary of State gave the worst showing during Tuesday night’s event.

Overall, the poll found Clinton with 45 percent support compared to 31 percent support for Sanders. That's a 3 point climb for Clinton and a 2 point uptick for her main rival.

NBC News/Survey Monkey found that Sanders is making in-roads with young voters, nabbing 54 percent of those below age 30. Clinton, in contrast, receives 24 percent among that same voting bloc.

The loser was Vice President Biden, who hasn't decided whether he's in the race but is thought to be nearing a decision. He won 10 percent in the poll, a downturn of 5 percent from his previous numbers in September. 

Other Democratic contenders fared worse, with only 1 percent saying they thought former Maryland Gov. Martin O’Malley (D) and former Rhode Island Gov. Lincoln Chafee (D) won the debate. Former Sen. Jim Webb (D-Va.) netted 0 percent.

NBC News and Survey Monkey conducted its latest survey last Tuesday-Thursday among 4,898 adults age 18 and over nationwide. It has a 2 percent margin of error.