The drama unfolded at about 3:20 p.m. at the Burger King restaurant in the 14600 block of NE 24th Street in Bellevue, police said.
The man was stabbed in the shoulder several times inside the busy restaurant, then staggered outside and collapsed on the sidewalk as stunned customers looked on.
The suspect took off running down 24th Street but was caught in the parking lot outside a nearby Safeway store and taken into custody after several customers called 911.
Medics responded and put the victim in an ambulance, but he died before they could take him to the hospital. Police say he was between 35 and 40 years old.
The restaurant was closed as customers and employees were interviewed by police, then allowed to leave.
Investigators are still trying to figure out what led to the deadly stabbing. The names of the victim and suspect were not immediately released.
Homicide is rare in Bellevue - police say they deal with only about one to two cases in the city per year.
The Burger King restaurant is scheduled to reopen later Monday.
Residents in the area said the stabbing would not deter them from eating at the Burger King restaurant where it happened.
"I wouldn't avoid that place just for that reason. It could have been anywhere," says Bob Bear, who has lived in the neighborhood there for decades.