Miami ? A mystery friend of O.J. Simpson’s slain ex-wife may have helped crack the case and a chatty Juice only dug himself in deeper, a police report reveals.

A woman caller claiming she knew O.J. and Nicole Brown Simpson called 911 with a tip that fingered one of his cohorts in the Las Vegas memorabilia heist.

Cops raced to the Las Vegas airport on Saturday, two days after the stickup, and nabbed Walter Alexander, a Simpson golfing buddy, before he could hop on a plane home to Arizona.

“You mean the O.J. thing?” Alexander, 46, asked cops when they confronted him as he tried to check in for the flight, the police report said.

Alexander, who the tipster said provided the guns for the heist, surrendered to cops and gave a statement after his lawyer got police to agree not to use the information against him.

Armed with the statement from Alexander, cops arrested Simpson the next morning, less than 24 hours after he confidently predicted to a New York Daily News reporter that the matter was “over.”

Simpson then made things far worse for himself.

He invited cops into his hotel room, and with his small dog at his side, held court – even though his lawyer warned him to zip his lips.

“I told him I could talk,” Simpson told detectives last weekend. “My lawyer said, ‘No, Juice.”‘

After ushering his girlfriend Christie Prody out of the room, Simpson insisted he would never have willingly parted with the prized memorabilia the dealers were hawking.

“My All-American ball!” Simpson exclaimed, referring to the memento of his award-winning college football season.

“I would never give that away,” he insisted.

The faded football great also kept on trying to explain away the botched heist as a big misunderstanding.

“Armed robbery! I knew I was going to be hearing from the cops,” he said, according to the report. “As p—–d as I was with them, it wasn’t that type of thing.”

Simpson was back home in Miami on Thursday after posting $125,000 bail on armed robbery, burglary and kidnapping charges.

He faces the possibility of decades in prison and will be back in court next month.

Cops said Simpson led a rag-tag posse of a half-dozen pals in a half-baked plan to grab a trove of sports memorabilia from a pair of dealers last Thursday.

Simpson was still trying to turn on the charm after cops arrested him, telling them he came to Vegas for a wedding.

Even after he was led out of his hotel in handcuffs, Simpson kept on trying to convince cops they got it all wrong.

“(Simpson) stated vehemently that he didn’t break into the room … so how could this be burglary,” the police report said.

“Simpson kept saying he didn’t do anything wrong and he was just getting his property,” the report continued.