Authorities came to that conclusion after realizing Sonnier's current girlfriend was Dixon's ex-girlfriend.
She told police Dixon had been harassing her, even after the relationship was over.
Police believe Dixon grew angry, but couldn't carry out a murder by himself.
"Dr. Dixon paid Mr. Shepard in silver bars to commit the murder as well as provide the murder weapon," Lubbock Police said.
Following Sonnier's death, an arrest warrant affidavit says Shepard was paid nearly $9,000 in silver.
A critical mistake was made that cracked this case wide open when Shepard tried to cash in one of the bars at an Amarillo Pawn Shop just days later.
"We have to upload data once a week to the "Leads Online" system which goes throughout the U.S., pawn shop owner Jeanette Damron said. "That way the police department is able to check those items against any items that are reported lost or stolen."
Certain items are required by law to be entered into the system. It's still unclear whether the silver bars belonged to Dixon, or if they were taken from Sonnier's home during the murder.
However, police confirmed he pawned a bar in exchange for $2,750.
Later, when authorities went to Shepard's home, they interviewed his roommate, who provided more incriminating evidence.
His friend told Lubbock PD that Shepard confessed to him about the crime before attempting to commit suicide.
That statement, was all police needed to put the pieces of this murder mystery together.
"Our hope is as the family holds Dr. Sonnier's funeral, that these arrests will begin to bring a sense of closure for them, as well as a sense of justice being done for Dr. Sonnier and his family," Lubbock Police said.
Both Dixon and Shepard are being held on $10,000,000 bond a piece.
Dr. Dixon is director of High Plains Plastic and Reconstructive Surgery, along with being the director and owner of Sensei Med Spa.
NewsChannel 10's calls for comment to his surgery center office were unsuccessful.
A voice mail said his office was closed Monday.
Dixon received a medical degree from Texas Tech in 1998 before he completed a residency in plastic surgery at Oklahoma University in 2003.
He is also listed as a clinical professor at the Texas Tech Health Sciences Center in Amarillo.