For nearly three hours on Tuesday, Donald J. Trump’s lawyer did his level best to persuade the jury to acquit his client, wielding a scalpel to attack nearly every strand of the criminal case against the former president.

Then it was a prosecutor’s turn. Rather than using a fine blade, he swung a sledgehammer.

Throughout a marathon closing argument that nearly outlasted daylight, the prosecutor delivered a sweeping rebuke of the former president, seeking to persuade the jury of 12 New Yorkers that Mr. Trump had falsified records to cover up a sex scandal involving a porn star. The prosecutor, Joshua Steinglass, wove together witness testimony and documents to drive home the key points of the weekslong case, the first criminal trial of an American president.

Facing the judge’s 8 p.m. deadline, Mr. Steinglass raced to the wire, stopping only to take a gulp of water as the sky darkened outside the towering courtroom windows.

“Everything Mr. Trump and his cohorts did in this case was cloaked in lies,” Mr. Steinglass said as the jurors, who had been glued to most of his presentation, began to fidget in their seats.

By the time the prosecutor finished, the courthouse had closed to other business and the traffic on Lower Manhattan streets had slowed. More than 10 hours after Mr. Trump’s lawyer began the day by calling the case “absurd” and “preposterous,” Mr. Steinglass finally had the final word.

The disparate strategies — Mr. Steinglass’s closing was more than twice as long as the defense’s — reflected their separate tasks. The defense needed only to establish reasonable doubt, while the prosecution needed to persuade the jury to accept a narrative that, Mr. Steinglass argued, could lead to only one ending: guilty on all counts.