On Tuesday night, after months of political heartburn, things finally started cutting Hillary Rodham Clinton’s way.

Her performance at the first Democratic presidential debate was so commanding that even her greatest vulnerability — the lingering controversy over her private email practices as secretary of state — ended up redounding to her benefit.

After she crisply explained that she made a “mistake” using a private email server and defended her judgment, the moderator, Anderson Cooper of CNN, turned to her biggest threat in the primary campaign so far, Senator Bernie Sanders of Vermont, in hopes that he would attack her. Mr. Sanders instead came to her aid.

“Let me say something that may not be great politics, but I think the secretary is right — and that is that the American people are sick and tired of hearing about your damn emails,” Mr. Sanders said to cheers and a standing ovation from the Democratic audience.