(CNN) — With the first Democratic debate in the books, a new CNN/ORC poll finds most who watched think Hillary Clinton had the best performance of the night, but her strong showing hasn’t boosted her standing in the race for the party’s nomination.

Clinton stands at 45 percent in the race for the Democratic nomination, with Vermont Sen. Bernie Sanders behind her at 29 percent. Vice President Joe Biden, who is considering a run for presidency and did not participate in last week’s debate, follows at 18 percent.

Behind the top three, former Virginia Sen. Jim Webb had 1 percent support, while former Rhode Island Gov. Lincoln Chafee, Harvard professor Larry Lessig and former Maryland Gov. Martin O’Malley all held less than 1 percent support.

Compared with pre-debate polling, Sanders’ support is up five points since mid-September, but no other candidate showed significant change.

As Biden mulls whether or not to get in the race, the poll suggests Democrats are becoming less enamored of a run from the vice president. In August, 53 percent of registered Democrats said they wanted Biden to run, that’s down to 47 percent in the new poll. Should Biden decide to sit out the race for the Democratic nomination, Clinton’s lead over Sanders climbs to 23 points: 56 percent would back Clinton, 33 percent Sanders.

Overall, 31 percent of registered Democrats say they watched all or most of the CNN/Facebook debate, held October 13 in Las Vegas. More than 6-in-10 Democrats who watched say Clinton did the best job, almost doubling the 35 percent who thought Sanders had the best performance. On the other side of the coin, 43 percent of those who watched said Chafee had the worst night, 31 percent thought Webb did, 12 percent O’Malley.

Among those Democrats who watched the debate, both Sanders and Biden are viewed more favorably than they are among Democratic voters generally: Sanders’ favorability number bumps from 62 percent among all Democratic voters to 84 percent among debate viewers, while Biden climbs from 76 to 89 percent favorable. Clinton’s numbers are about the same in both groups.

Despite their positive feelings toward Biden, debate-watchers are more apt than others to say Biden should stay out of the contest (61 percent think he should not run, compared with 43 percent of those who did not watch) and they are far more likely to be satisfied with the Democratic field generally (84 percent compared with 64 percent among those who didn’t watch).

Assessing the lesser-known candidates, debate-watchers are more positive than other Democrats toward O’Malley, (44 percent favorable compared with 20 percent among Democratic voters generally). But Webb and Chafee are both viewed more negatively among those who watched (For Chafee, 32 percent unfavorable among debate-watchers vs. 18 percent among all Democratic voters; Webb is at 37 percent unfavorable among debate-watchers, 20 percent among all Democratic voters).

Following the debate, Clinton continues to dominate as the more trusted candidate across several top issues, with double-digit advantages over Sanders and Biden as the candidate who would best handle the economy, health care, foreign policy, race relations, climate change and gun policy. Clinton also now holds a small edge over Sanders as most trusted on income inequality (43 percent Clinton, 38 percent Sanders).

Debate-watchers are more likely than others to say they trust Sanders on top issues, though even among this more-friendly audience, he continues to trail Clinton on most issues. Exceptions are income inequality (50 percent of debate-watchers trust Sanders vs. 36 percent for Clinton) and climate change (40 percent each say Clinton and Sanders would be best able to handle that).

Sanders gained no ground, however, on foreign policy. On that question, Clinton’s strength grows among those who watched: 77 percent in that group say they trust her most to handle foreign policy, up from 66 percent among Democratic voters overall.

On two issues where the debate highlighted differences among the candidates, fissures within the Democratic electorate on who would best handle them emerge.

Income inequality appears to be the most divisive issue, with women, older voters, those without college degrees, moderates and those with lower incomes more apt to trust Clinton on the issue, while those with college degrees, liberals, and urbanites are more likely to favor Sanders.

And on gun policy, there’s a sharp gender divide. Women are far more likely to say they trust Clinton to handle it than men, 50 to 37 percent. Democratic gun owners are more evenly split on the question, with 35 percent saying they trust Clinton most on gun policy, 27 percent Sanders and 21 percent Biden. Among those Democrats who do not own guns, it’s 48 percent Clinton, 21 percent Biden and 16 percent Sanders.

Overall, Democrats aren’t much more satisfied with their field now than they were in July before any debates had happened. While the share “very satisfied” has risen from 26 to 33 percent, the share saying they are at least fairly satisfied has held steady at about 7-in-10. Women do report feeling more satisfied with the field than men, but younger Democrats, a key group for Barack Obama’s general election victories, are far less satisfied with this field of candidates than older Democrats. Only about one-quarter of those under age 50 say they are very satisfied, compared with 40 percent of those age 50 or older.

When matched against the top candidates from the Republican field, Clinton, Sanders and Biden all top Donald Trump, who has been leading most polling on the Republican nomination contest since this summer. But Biden is the only one who holds a significant lead over Ben Carson, a more recent addition to the top of the Republican field. Trump trails Clinton by 5, Sanders by 9 and Biden by 10. But against Carson, both Clinton (47 percent to Carson’s 48 percent) and Sanders (46 v to Carson’s 48 percent) run about evenly with the former neurosurgeon. Biden tops Carson by 8 points.

The CNN/ORC International Poll was conducted by telephone October 14-17 among a random national sample of 1,028 adult Americans. Results among the 425 registered voters who say they are Democrats or independents who lean toward the Democratic Party have a margin of sampling error of plus or minus 5 percentage points.

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