The "Ghost Adventures" star tells TMZ that upon looking into the eyes of Lilly the doll -- during a recent visit to the museum -- the man fainted and bashed his head on the display stand -- and we've got the chilling moment on camera.

Zak says the man received medical attention after regaining consciousness and was OK -- although, disturbingly, he wouldn't speak to anyone afterward, let alone even look at any of the museum staff.

The man promptly fled the museum and has not returned since.

An Oregon-based antiques dealer first found Lilly under an old steamer trunk -- and took it back to his store where he immediately began having nightmares about a little girl dying a violent death.

Later, when a young girl visited the store, she told her mother she had a convo with "the girl inside of Lilly, who said she died in a scary way."

Zak traveled to the shop to investigate ... and when the woman working behind the counter took Lilly down from the shelf, she immediately doubled over with abdominal pain ... chanting, "I must wash my hands" repeatedly.