It's because Sarutobi was the Fourth's father, and Naruto is the Fourth. The fourth obviously sealed Kyuubi into his own stomach, much like Akatsuki is trying to do. But Kyuubi turned him into a baby.

This is also why the Fourth wanted the village to look upon Naruto as a hero. And why Sarutobi chastised Anko for wishing the Fourth 'were here' and ready to fight. And why Orochimaru is afraid of Naruto.