Washington (CNN) Hillary Clinton maintains a commanding lead in a new CNN/ORC poll , boosted by broader support in the days after the latest debate between the remaining three Democratic presidential candidates.

Overall, Clinton tops Sanders among registered voters who are Democrats and Democratic-leaning independents 50% to 34%. That's a slightly tighter margin than in late-November, when Clinton led 58% to 30% over Sanders

But those overall results mask a shift back toward Clinton following the Democratic debate on Saturday night. In interviews conducted before the debate, Sanders ran closer to Clinton, with 37% support to Clinton's 45%. Among those interviewed after the debate, Clinton's lead grew to 60% vs. Sanders' 27%.

The Sanders campaign focuses heavily on economic issues, and the new poll suggests he has boosted his standing on that issue. Yet Sanders continues to trail Clinton as the candidate better able to handle economic issues, 47% say they think Clinton is best able to handle it, 39% Sanders.

The former secretary of state has even larger leads on foreign policy matters and ISIS, however, topping Sanders 72% to 15% on foreign policy, 63% to 18% on ISIS. Clinton also holds a 21-point advantage over Sanders on handling gun policy, 51% prefer Clinton vs. 30% Sanders.

Although much of the debate over guns on the Democratic side has centered on Sanders' more gun-friendly views after representing a state where many own guns, among registered Democrats who say they or someone in their household owns a gun, Clinton is more widely trusted to handle gun policy: 58% favor her take on the issue vs. 28% who prefer Sanders.

Clinton's favorability rating holds steady in the new poll compared to earlier in the fall, with 47% of adults viewing her favorably and 51% unfavorably.

Among registered Democrats, 77% have a favorable take, about the same as the 78% viewing her positively in October. Sanders, who was less well known in October, has seen an uptick on both the positive and negative sides of his favorability ledger, 46% now hold a favorable opinion, 36% unfavorable. Among registered Democrats, 74% have a positive take, up from 62% in October.

The gender gap that has persisted throughout the race for the Democratic nomination continues as the year comes to a close, with women favoring Clinton 56% to 23% and men about evenly divided, 46% Sanders to 44% Clinton. The gap is actually even larger when it comes to favorable views of the candidates: 82% of Democratic women hold a favorable view of Clinton, but that drops to 71% among men. And on Sanders, 84% of men hold a positive impression vs. just 64% of Democratic women.

Despite those gaps, Democratic men are actually more likely than Democratic women to say the party has a better chance to win in 2016 with Clinton than without her (64% of men say the best chance is with Clinton, 55% of women say the same). Overall, about 6 in 10 Democratic voters say the Democratic Party has a better chance of winning the presidency with Clinton as their nominee than with someone else (59% say the party has its best chance with Clinton, 38% someone else).

Democrats are more apt to see Clinton as holding several key attributes than they are Sanders. Nearly nine in 10 see Clinton as having the right experience to be president (89%), three-quarters call her someone they would be proud to have as president (76%), and 7 in 10 as someone who shares their values (72%). Smaller majorities say the same about Sanders, with the smallest gap coming on shared values (62% experience, 63% proud, 67% values).

Among all registered voters, Clinton tops the five Democratic and Republican candidates tested in the poll on experience (62% of voters say she has the right experience to be president) and as someone you would be proud to have as president (44%, not significantly ahead of Rubio at 43%). On values, Sanders tops the field with 43% of voters saying the Democratic socialist shares their values, narrowly topping Clinton (42%) and Rubio (42%).

The poll, however, suggests Clinton faces a stiff challenge from each of three Republicans at the top of the field. She narrowly tops Donald Trump within the poll's margin of sampling error, 49% to 47%, in a hypothetical general election matchup. But she falls behind Ted Cruz by 2 points (Cruz 48% to Clinton 46%, a shift since last month when Cruz trailed Clinton 50% to 47%) and 3 points behind Marco Rubio (49% Rubio to 46% Clinton). Among independent voters, Clinton trails Rubio and Cruz by 12 points each, while running even with Trump.

The CNN/ORC poll was conducted by telephone Dec. 17-21 among a random national sample of 1,018 adults. Results for the full sample have a margin of sampling error of plus or minus 3 percentage points. For results among the 414 registered voters who are Democrats or independents who lean toward the Democratic Party, the margin of sampling error is plus or minus 5 percentage points.