There was no parallel in modern American history, with insurgents acting in the president’s name vandalizing Speaker Nancy Pelosi’s office, smashing windows, looting art and briefly taking control of the Senate chamber, where they took turns posing for photographs with fists up on the dais where Vice President Mike Pence had just been presiding.

By the time the Senate reconvened late on Wednesday evening, hours after lawmakers had been evacuated from a Capitol overrun by rebels carrying pro-Trump paraphernalia, one of the nation’s most polarizing moments had yielded an unexpected window of solidarity. Republicans and Democrats locked arms to denounce the violence and express their determination to carry out what they called a constitutionally sacrosanct function.

“To those who wreaked havoc in our Capitol today, you did not win,” Mr. Pence said in a sharp break from Mr. Trump, who had praised the mob. “Violence never wins. Freedom wins. And this is still the people’s house.”

Senator Mitch McConnell, Republican of Kentucky and the majority leader, said the “failed insurrection” had only clarified Congress’s purpose.

“They tried to disrupt our democracy,” he said. “They failed.”

The upheaval unfolded on a day when Democrats secured a stunning pair of victories in runoff elections in Georgia, winning effective control of the Senate and the complete levers of power in Washington. And it arrived as Congress met for what would normally have been a perfunctory and ceremonial session to declare Mr. Biden’s election.

The siege was the climax of a weekslong campaign by Mr. Trump, filled with baseless claims of fraud and outright lies, to try to overturn a democratically decided election that he lost.

“We gather due to a selfish man’s injured pride, and the outrage of supporters who he has deliberately misinformed for the past two months and stirred to action this very morning,” Senator Mitt Romney, Republican of Utah and the 2012 presidential nominee, said after the chamber reconvened. “What happened here today was an insurrection incited by the president of the United States.”

Wednesday evening, Mr. Biden, seeking to tamp down the anarchy that Mr. Trump stoked with angry language just hours earlier, Mr. Biden urged rioters to abandon what amounted to an armed occupation of the House and Senate. The president-elect denounced Mr. Trump’s refusal to graciously accept defeat, and suggested that the president was to blame for the violence.

“At their best, the words of a president can inspire,” Mr. Biden said. “At their worst, they can incite.”

Far from discouraging confrontation, Mr. Trump had encouraged his supporters earlier Wednesday to confront Republican lawmakers going against him to side with the Constitution.