Airport spokesman Perry Cooper said the man, who is in his late 20s, was at checkpoint five in concourse D when he sprinted past security agents.
Police and TSA agents gave chase, but the man somehow ended up outside on the tarmac.
Once the man was on the tarmac, he raced up a stairway and punched through a window in a door at the end of a jetway connecting the empty plane with the terminal, Cooper said. He crawled through the broken window glass and entered the unoccupied plane.
"He had to be tackled to the ground," the spokesman said, adding the arrested man suffered minor injuries. Cooper said officers were unhurt.
The man was booked into King County Jail on suspicion of trespassing and assault on a police officer.
The breach didn't impact airport operations.