Related Cos. chairman Stephen M. Ross just pulled off a strategic coup against the organized labor bloc he’s battling with over Hudson Yards.

He’s gotten the largest union, which represents carpenters, to split ranks from the others — allowing the developer to negotiate directly with the carpenters without first having to sign a multi-union project labor agreement, or PLA.

Related’s surprise deal with the powerful United Brotherhood of Carpenters, or UBC, and its local affiliate, the New York City District Council of Carpenters, could give Related more flexibility in work rules and hiring for the site’s next major new building, 50 Hudson Yards, and on the 28-acre complex’s yet-to-come western portion.

BlackRock is the largest tenant at 50 Hudson Yards, a $4 billion tower at 10th Avenue between West 33rd and 34th streets to be completed in 2022. Work on the complex’s western yard between 11th and 12th avenues is to start in 2019.

What both parties call a “historic partnership” between Related and the carpenters appears to give Related the upper hand in its ongoing battle with the Building and Construction Trades Council of Greater New York, an umbrella group representing 100,000 workers from 15-odd building construction unions.

A PLA requires that a developer use 100 percent union labor in exchange for concessions to reduce construction costs and for a no-strike guarantee. Related signed a PLA with the BCTC for the first Hudson Yards buildings in 2013.

But instead, the unions inflated costs by $100 million, Related said in lawsuits filed against the BCTC and its president, Gary LaBarbera — whom the developer blames for disavowing responsibility for actions by individual unions.

“If Gary can’t enforce what his members agreed to, why should we make another deal with him?” a Related insider asked.

LaBarbera wanted all the unions to demand a new PLA with Related and fought to prevent defections. But now that the carpenters have broken ranks, the coalition could fall apart.

In a lawsuit it filed earlier this year, Related said the unions reneged on the 2013 PLA, which covered construction of the first group of Hudson Yards skyscrapers as well as for the site’s retail portion.

Despite a previously warm relationship with LaBarbera, Related said in a second lawsuit against the BCTC that he winked at “thuggish” and “corrupt practices” by the unions, including no-show jobs, time-sheet fraud and such irregularities — exposed by The Post — as paying a worker whose only job was to deliver coffee $42 an hour.

The disputes spilled over into loud anti-Related demonstrations and at least one illegal strike. The National Labor Relations Board in July ordered one union, Steamfitters Local 638, to end an illegal “sympathy strike” at 55 Hudson Yards.

Related built 55 Hudson, a tower opening this fall with a roster of A-list hedge funds and law firm tenants, without a PLA. Although 92 percent of workers on the job were union members — and although Related claims to be the largest private-sector union employer in the city, including 20,000 union members working at Hudson Yards over the past six years — it wasn’t enough for the BCTC.

Related and the carpenters union say their new arrangement — described as a “progressive new industry model” — will create millions of man-hours of work for members.

Specifics of the “progressive” relationship weren’t spelled out. But it was to include “work rules that reflect present-day techniques, materials and technology; opportunities for entry-level positions; and blending of skilled and unskilled levels to achieve economic efficiencies.”

In a seeming expression of sympathy for Related, UBC General President Douglas J. McCarron said, the carpenters and the developer “share a common goal of creating not only good-paying and safe jobs, but also a mechanism for opportunity, training and professional growth.

“The old approach limited advancement opportunities and created inherent inefficiencies for us and our contractors. This new model reflects the future of union labor in New York,” McCarron added. “This type of creative thinking should be replicated throughout the city and the industry.”

The carpenters’ New York unit’s executive secretary-treasurer, Joseph Geiger, said his organization “and the unionized construction industry as a whole, cannot remain stuck in the ways of the past while the industry evolves around us.

“We are pleased to work with Related, which has shown a deep commitment to enhance opportunities for current skilled members and future members.”

Related Cos. President Bruce Beal Jr. said, “We appreciated our ongoing relationship with the UBC and the NYCDCC and their willingness to think outside the box in a progressive way.”