The man was Kenneth Boonstra, 48, who also lived in the town about 30 miles east of Seattle, King County sheriff's Sgt. Katie Larson said in a statement.
Larson said investigators are confident Boonstra is the same man who broke into the home 12 hours earlier and assaulted and robbed the woman. The spokeswoman said detectives are awaiting DNA testing results for positive confirmation.
Boonstra has no criminal history that the sheriff's office is aware of, Larson said.
The King County medical examiner's office said Tuesday that the man died of multiple stab wounds.
The couple suffered no significant injuries from the fight. The sheriff's office has not identified them.
Investigators don't believe the residents knew the intruder, and there's nothing to indicate why the house was attacked or why the man returned, Sgt. Cindi West said earlier.
The couple's baby daughter and the wife's mother were also in the home at about 1:40 a.m. Monday when the couple were awakened by barking dogs.
The man went to check on the dogs and was confronted by the intruder. They started fighting, and the wife grabbed a knife and jumped in to help. The intruder died at the scene, the sheriff's office said.
On Sunday afternoon, an intruder entered the house through an unlocked door when the wife was home with her daughter and mother. The robber assaulted the younger woman and got away with cash.
She didn't get a good look at him because her hair was grabbed from behind, West said. She was slapped and punched in the face and suffered an ankle injury as she was dragged by her hair.