As camera shutters clicked, Mr. Skipworth fell into the arms of his wife, Melissa, and son Christopher, 8, and then hugged Ms. Lawrence. He takes office on Tuesday.

The graciousness shown by the candidates, both of whom accepted the outcome, wasn’t lost on anyone at the ceremony, which happened one day after a violent mob, egged on by President Trump’s refusal to accept his election loss, rampaged through the Capitol and disrupted Congress as it was certifying Joseph R. Biden Jr.’s victory.

“It was palpable,” Mr. Foreman said. “You realize, ‘Hey, there’s all this stuff going on nationally, but here they are — friendly, gracious, there’s no us against them. It was all of our residents and citizens coming together. It was a cool, friendly atmosphere, and I was proud of that.”

Ms. Lawrence, who was running for office for the first time, said the loss was a heavy blow but also a relief after a tough, 10-month campaign. She said she had had a feeling that she was going to lose the drawing.

“I had respect for Sean, and I knew if I was going to lose, I was going to lose with grace,” she said. “This is about our community. This is not about me winning or him winning. It’s about how we get something done for our citizens.”

Mr. Skipworth said he was moved by Ms. Lawrence’s hard work and civility.

“Given what happened, it is refreshing for people to see this in everyday America,” he said. “At the end of the day, we came and hugged it out and shook hands, and that was it. And that’s how it should be.”

Still, Mr. Skipworth said he wanted to amend the City Charter to ensure that if a future election ends in a tie, it prompts another election, not a random drawing. He said he planned to turn his strange victory into an object lesson for his students on the importance of voting.

“Every vote counts,” he said, “and I’m living proof of that — literally.”

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