After two weeks of enthralling jurors with stories of sex and scandal, prosecutors delved into the documents at the heart of the criminal trial against Donald J. Trump on Monday, a pivotal turn in the case that came on the same day the judge held Mr. Trump in contempt and threatened to jail him.

After the judge rebuked Mr. Trump for violating a gag order and mounting “a direct attack on the rule of law,” the prosecutors elicited crucial testimony from witnesses who tied the former president to an infamous payment.

Mr. Trump made the payment to his longtime fixer, Michael D. Cohen, reimbursing him for a $130,000 hush-money payoff to a porn star, prosecutors say. When Mr. Trump repaid Mr. Cohen, prosecutors say, the then-president falsified records to cover up the payoff to the star, Stormy Daniels.

When questioning one of the witnesses — Jeffrey S. McConney, Mr. Trump’s former corporate controller — prosecutors provided jurors with their first look at some of those records, including monthly invoices Mr. Cohen submitted to Mr. Trump’s company. The invoices claimed that Mr. Cohen was repaid for “legal expenses” that arose from a “retainer agreement.”

But prosecutors say the purported expenses and retainer agreement were works of fiction. And although Mr. McConney testified that he did not know the true nature of the payments, he bolstered the prosecution’s contention that the records were fishy.