Perhaps Naruto has been training with a new technique that we don't know about in the original Naruto series. He could use this new skill to counter the fire ball. For example, he might have learned a water - based jutsu that can extinguish the fire ball easily. He could also call upon his friends for help. For instance, Sasuke could use his Sharingan to predict the trajectory of the fire ball and help Naruto save Ami more effectively.
Naruto is known for his quick thinking and determination. In this fanfiction scenario, he could potentially use his Nine - Tails chakra to enhance his strength and durability. He might jump in front of Ami and take the hit of the fire ball himself, but then use the Nine - Tails' healing ability to recover quickly. Another way is that he uses his knowledge of the area to find a hiding place for Ami and lead her there before the fire ball reaches them.
Well, in most cases, Naruto might use his signature jutsu like the Rasengan. He could either deflect the fire ball with it or use his incredible speed to get to Ami before the fire ball hits her. Maybe he also uses his shadow clones to create a distraction for the attacker while he rescues Ami.