Corporation Counsel Zachary Carter finally does what he should have from the start – let probers have access to the mayor’s computer.

The stonewall erected by Mayor de Blasio to impede a probe into how the city helped a developer make a $100 million real-estate killing has cracked. De Blasio was happy to have the Department of Investigation look into the complex transaction as long as the agency, headed by his former campaign treasurer, focused on functionaries out in the netherlands of the bureaucracy.

But when DOI followed the trail to the mayor and top aides, de Blasio took the stunning and unprecedented step of denying investigators access to City Hall records and computers.

He tried to skate by brazenly claiming that top lawyer Zachary Carter had divined solid legal rationales for concealing evidence. Carter, too, insulted the intelligence with such mumbo-jumbo.

Now, though, after DOI Commissioner Mark Peters approved an equally stunning ultimatum to the mayor, via a letter to Carter — come clean or come to court — Carter ended the coverup.

As first reported by Greg Smith of the Daily News, Carter has agreed to turn over to DOI “all digital information” on the computers of the mayor, First Deputy Mayor Anthony Shorris, Director of Intergovernmental Affairs Emma Wolfe and Shorris’ chief of staff, Dominic Williams.

So much for the mayor’s preposterous dodge that city agencies sometimes butt heads.

“I think it’s totally normal — two different institutions with two different jobs to do,” the mayor yawned as DOI was discovering highly relevant evidence of who knew what when that Carter had sealed on disingenuous, if not false, grounds.

The case involves an old school building on the Lower East Side, long ago deeded to the operator of an AIDS-related nursing home, with the deed limiting the property to such a use.

After demand for its services fell, the operator asked the city to lift the deed restrictions with the help of lobbyist James Capalino, an old friend of Shorris and big contributor to the mayor’s Campaign for One New York.

Capalino’s sway sparked high-level City Hall deliberations, including consideration of using the building for housing, until health-care workers’ union Local 1199, de Blasio’s most generous backer, protested a loss of jobs.

At that, Shorris & Co. lost interest and the city marched toward lifting the deed restrictions for a payment of $16 million. A developer then sold the property for $116 million.

In a report issued on July 14, DOI found unaccountable sloppiness and revealed City Hall’s stonewalling. Meanwhile, according to a letter sent to Carter by Inspector General Jodi Franzese, DOI discovered that documents Carter had kept secret included a memo recommending against lifting the deed restrictions written by a City Hall staff member after a meeting with a deputy mayor.

Although directly on point, Carter had claimed the memo was irrelevant — a claim that was not his to legally make.

DOI chief Peters has stepped aside from probes involving de Blasio’s fundraising. Here, he empowerd staff to vindicate the agency’s authority and stood up for the public interest.