Seattle cops cooked up a fake chewing gum “survey” to trick a homeless man into giving a DNA sample and then arrested him in connection with the murder of Maine woman 36 years ago.

Gary Sanford Raub was busted on Monday on suspicion of brutally stabbing Blanche M. Kimball in her Augusta home in 1976.

Seattle investigators provided few details about the chewing gum ruse, only saying that Raub’s DNA matched some taken from a knife and blood at the scene of the 70-year-old Kimball’s death, The Seattle Times reported.

“This case has been worked over for over three decades,” Maine State Police spokesman Steve McCausland told the newspaper.

“The DNA was significant in bringing the case to this point.”

Raub, 63, who changed his name from Gary Wilson and has a long rap sheet going back to his teen years, was being King County Jail on $1.5 million bond pending extradition back to Maine.

He served prison time in Washington after getting convicted for third-degree rape in 1982, Seattles KIRO television reported.

Police went looking for Kimball after neighbors reported her missing, and she was found dead in her home on June 12, 1976, with more than 40 stab wounds and cuts on her body, according to a medical examiner’s report.

Kimball, a retired dental technician and nurse, was known to take in boarders and Raub was renting a room from her at the time, Maine’s Press Herald newspaper reported.

Her murder was the state’s oldest unsolved homicide case, the newspaper said.

Raub was charged with first degree murder and expected to appear in court on Wednesday.