Perhaps Anko is trapped in a genjutsu and Naruto uses his own experience with breaking free from illusions to save her. He could sense her distress and use his chakra to disrupt the genjutsu, freeing Anko. This would show Naruto's growth and his ability to help those in need, even a more experienced ninja like Anko.
Perhaps in this fanfiction, Naruto has some sort of special power or transformation that he unlocks just in time to face Orochimaru. It could be related to his Nine - Tails chakra in a new and unique way. He uses this power to break through Orochimaru's defenses and save Hiruzen. Naruto might also use his knowledge of Orochimaru's weaknesses that he has learned either from Jiraiya or from his own past encounters with Orochimaru's minions.
I'm sorry I haven't read a specific fanfiction with this exact plot, but generally in such a scenario, Naruto would probably use his powerful jutsu like Rasengan. He'd sense Hinata in danger from Orochimaru, rush to the scene, and engage in a fierce battle with Orochimaru to rescue Hinata. Maybe he'd also get some help from his friends along the way.
One possibility is that Anko is poisoned during a mission. Naruto, having learned some medical ninjutsu from Tsunade, uses his skills to find an antidote and save her. He might have to search far and wide, facing various challenges along the way.
In a 'naruto saves anko' fanfiction, Naruto might find Anko in a dangerous situation like being trapped in a genjutsu by a rogue ninja. Naruto, with his strong will and Uzumaki chakra, could break the genjutsu and save her. He'd then comfort her and they might form a stronger bond, leading to Anko having more faith in the new generation of ninja.
Naruto's character might develop a stronger sense of purpose. Saving Sasuke becomes more than just about their friendship; it could be about righting a wrong in the ninja world. His resolve to save Sasuke would make him train harder and become more strategic in his battles.
One possible scenario could be that the Anbu arrives just in time as Anko is about to use a dangerous jutsu on Naruto. The Anbu might use their superior speed and stealth to disarm Anko and rescue Naruto. Another scenario could be that the Anbu has been secretly observing Anko's actions towards Naruto, suspecting her of having some malicious intent. So they step in when they see Anko cornering Naruto. Maybe the Anbu uses some special ninjutsu to create a diversion and then whisks Naruto away to safety.
One possible plot twist could be that Orochimaru was actually being controlled by a greater evil, and Naruto has to not only save Hinata but also deal with this hidden threat. Maybe Orochimaru was forced to target Hinata to draw Naruto out for this other entity's purposes.
One possible scenario could be Naruto arriving just in time as Orochimaru is about to perform a dangerous jutsu on Sasuke. Naruto uses his new Rasengan variant, overpowering Orochimaru and rescuing Sasuke. It would be a very action - packed moment.