After graduating from Nara Ikuei High School in 1995, he joined J. League side Yokohama Flügels. He became the No.1 GK for the club in August of that season. His first game was on August 16, 1995 in a league match against Bellmare Hiratsuka.
He played for Japan as the No.1 goalkeeper because Kawaguchi was injured. However, Narazaki himself got a broken finger in 2009. After it healed, he was named in the 2010 World Cup squad. He was one of two Japanese players (the other being Kawaguchi) to play in 4 World Cups in a row. However, even though he played well in the qualifiers, he did not play in the tournament. Eiji Kawashima was played instead. He played once more for Japan when he captained the team to a 2-1 victory over Guatemala on 7 September 2010. He then retired from playing for his country.