One bill - which has been stored away all these years - had fresh blood on it.
Now, 21 years later, DNA technology has matched that blood to Griffin, linking him to the robbery and slaying of 22-year-old Bradley Newell Perry.
A sketch of the suspect, drawn by a gas station customer, also matches Griffin, according to police.
On Thursday, Box Elder County prosecutors charged Griffin, a 47-year-old Logan resident, with aggravated robbery and capital murder, which carries a possible death penalty.
Box Elder County sheriff's investigators said Griffin - currently serving time in federal prison in California for a weapons violation - was implicated with the help of the national DNA database known as CODIS.
Chief Deputy J. Lynn Yeates said arrangements were being made to extradite Griffin to Utah for prosecution.
"We're very happy we've come to this conclusion, rather than leaving it a cold case," Yeates said.
The case was investigated heavily after the May 26, 1984, slaying, then re-opened in 1997. Over the years, more than 300 suspects have been scrutinized.
Griffin is the first to be charged with murder, but perhaps not the last. Police believe there may have been accomplices at the Texaco Short Stop Convenience Store that night, and the investigation is ongoing.
In 2003, sheriff's detectives tried to revive the case by charging prison inmate Craig Lee Martinez, 35, with related crimes of obstruction of justice and witness tampering. A judge dismissed the charges, saying the evidence was weak.
The dead man's family issued a statement on Thursday, saying that they appreciated the work of law enforcement and hoped Griffin's arrest would bring them closure.
Valerie Odenthal, the victim's sister, said in an interview that her younger brother was a returned Mormon missionary, "a spiritual person, a peacemaker."
Engaged to be married, Perry was attending Weber State College, hoping to become a radiologist and working part-time at the gas station.
"It wasn't even his night to work," Odenthal said. "He took someone else's shift because he wanted a little extra money to get ready to get married.
"He was a good kid, who'd do anything for anybody," she added. "He was this Eagle Scout kind of person who loved people and worked hard to help others."
According to court documents, Perry was stabbed with a screwdriver-type instrument and a short-bladed knife. His hands were tied behind his back and he was hit in the head with a 60-pound cylinder.
Two Utah State University students arrived at the station about 4 a.m., which was during or immediately after the slaying, according to police.
Though it was a self-serve station, a man, now believed to be Griffin, came out and waited on the students. Observing blood on the man's arm, shirt and shoes, they drove 6 miles down the road and called the sheriff's office.
Perry's body was found in a back room. About $100 was missing from the cash register.
The state medical examiner reported multiple defensive wounds on Perry's hands, including a nearly severed finger.
Griffin has been in and out of Utah State Prison since 1990 on drug and burglary convictions and repeated parole violations, according to Utah Board of Pardons and Parole records.
The Logan Police Department said Griffin has a criminal record of 27 arrests.
In 2003, parole authorities terminated Griffin's sentence, releasing him without further supervision. But later that year, he was slapped with federal weapons charges for being a convicted felon in possession of ammunition.
Police serving an outstanding warrant at Griffin's Logan home found 20 rifle bullets, 26 shotgun shells and drug paraphernalia. He was indicted in July 2003 and sentenced in May 2004 to 34 months in a federal prison.
Melodie Rydalch, spokeswoman for the U.S. Attorney's Office in Utah, said Griffin's prosecution was part of "Project Safe Neighborhood," an anti-gun violence initiative in which federal, state and local authorities work to take chronic troublemakers off the streets.
Rydalch said more than 1,000 cases have been prosecuted in the past five years as a result of the initiative.