The narrow ruling came less than 48 hours before the start of the FedEx Cup playoffs in Memphis, but the broader turmoil could last for years.A federal judge on Tuesday rebuffed an effort by three LIV Golf players to compete in this week’s FedEx Cup playoffs, giving the PGA Tour interim support as it faces an uprising over the invitational series financed by Saudi Arabia’s sovereign wealth fund.The decision was an early, if narrowly tailored, victory for the PGA Tour’s efforts to undercut LIV Golf, which has spent recent months draining the more established tour of some of the star power it relies on to draw fans, television money and sponsorships.Although 11 players, including the major champions Phil Mickelson and Bryson DeChambeau, sued the Tour last week over its decision to bar them from its competitions, only three — Talor Gooch, Matt Jones and Hudson Swafford — asked Judge Beth Labson Freeman of the U.S. District Court for the Northern District of California to order that they be allowed to compete in the playoffs, which will begin on Thursday at T.P.C. Southwind in Memphis.Judge Freeman, near the end of a Tuesday afternoon hearing in San Jose, Calif., said that she did not believe the players would suffer “irreparable harm” if they were not allowed to play, a vital legal standard to secure a temporary restraining order.The players’ guaranteed-pay contracts with LIV Golf, she said, made it likely that they would “be earning more than they have made and could reasonably have expected to make in a reasonable period of time” with the PGA Tour.Moreover, she said, the arrangements between LIV Golf and the players had been negotiated with the potential loss of PGA Tour compensation in mind.Gooch, Jones and Swafford have combined for more than $37 million in career earnings, according to PGA Tour data.But the players, in a court filing last week and in San Jose on Tuesday, argued that the PGA Tour had defied its internal rules to exclude them from an event that leads to one of golf’s most lucrative paydays. The playoffs, scheduled to conclude late this month, can also clear the way for a player’s participation in men’s golf’s major tournaments: the British Open, the Masters Tournament, the U.S. Open and the P.G.A. Championship.“Large bonuses, big purses, substantial retirement plan payments, sponsorship, branding, and important business opportunities are at stake,” lawyers for the players wrote in a motion. The PGA Tour’s suite of tactics against LIV Golf and its players, they asserted, “are obviously anticompetitive, as they serve no purpose but to thwart competition and maintain its monopsony.”The PGA Tour, in a filing on Monday that condemned LIV as “a strategy by the Saudi government to use sports in an effort to improve its reputation for human rights abuses and other atrocities,” insisted that “antitrust laws do not allow plaintiffs to have their cake and eat it too.”LIV golfers, the filing suggested, could not expect to cycle between LIV events and PGA Tour competitions and break “contracts without consequence.”Besides, PGA Tour officials asserted, the players waited until the playoffs’ start was imminent to bring a legal challenge, effectively conjuring an emergency for Judge Freeman to consider.“Their ineligibility for Tour events was foreseeable when they accepted millions from LIV to breach their agreements with the Tour, and they knew for a fact that they were suspended on June 9,” the PGA Tour wrote, adding that other players who qualified for the playoffs and joined the lawsuit had not challenged their exclusions. (A lawyer for the players, Robert C. Walters, told Judge Freeman on Tuesday that the nature of the suspensions became clear only last week.)Tuesday’s ruling was an early one in the turmoil that could shadow golf for years, in part because the litigation could prove protracted. Away from the courthouse, LIV has announced plans to expand to 14 events in 2023, up from eight this year. It has also said it will offer $405 million in purses next year, compared with $255 million this year, for events expected to include such players as Dustin Johnson, Sergio García and Brooks Koepka.The players suing the PGA Tour include Phil Mickelson, who played last month in the LIV event at Trump National Golf Club Bedminster, a New Jersey course owned by former President Donald J. Trump.Doug Mills/The New York TimesThe PGA Tour, determined to preserve its standing as the pre-eminent circuit for professional male golfers, has suspended defectors, and some organizers of the major tournaments have signaled that they could try to keep LIV players out of their 2023 fields. The PGA Tour’s efforts have led to scrutiny: The Justice Department has been exploring whether the strategies ran afoul of federal antitrust laws, a particularly sensitive subject for professional and collegiate sports organizers in the United States.Even as LIV has attracted some of golf’s best-known figures, the PGA Tour has maintained a reservoir of support among elite players. Tiger Woods criticized LIV on the eve of last month’s British Open, where organizers made plain that Greg Norman, the LIV chief executive and a two-time Open champion, was unwelcome. Rory McIlroy and Justin Thomas, who have a combined six major titles, have also been among the most forceful Tour loyalists.Norman told Fox News Channel this summer that LIV had offered Woods “in the neighborhood” of $700 million to $800 million if he joined the series.Gooch, Jones and Swafford command far less attention. Gooch, ranked 20th in the playoff standings, finished in a tie for 34th at the British Open in July, but his career-best showing in a major was a tie for 14th.This year’s Masters marked the first time Swafford, 67th in the playoff standings, survived the cut at a major. Jones, 65th in the playoff rankings, missed weekend play at the only major he contested in 2022, the P.G.A. Championship.The men have not qualified for next year’s majors. When the players asked Judge Freeman to intervene, their lawyers said that keeping them from the playoffs would likely doom their chances of competing in those tournaments, starting with the Masters in April.In a statement on Tuesday, LIV Golf said it was “disappointed” by the judge’s ruling.“No one gains by banning golfers from playing,” the statement said. More