The first time Naruto used Rasengan without clones or chakra hands is in Naruto episode 134 at around 8:20 (YouTube video). He first used Rasengan with only one hand although he is assisted by Six-Tails chakra.
I believe it was after Naruto got half of the Sage of Six Path Chakra, mainly because in part one (ep. 135), he had the cloak of the Nine-Tails to help him, so he wasn't conscious of it. I think he was conscious of it when he fought Sasuke because he did multiple shadow clones with Rasengan. Also because of the half he received, he could naturally learn Chakra control (thus how to use Rasengan with one hand).
When Naruto and Sasuke were fighting in episode 134, Sasuke let his curse mark's power activate. He knew that the power would soon eat away his body, so he planned to finish off Naruto with a Chidori. However, when the Nine-Tails' cloak took over Naruto's body, he didn't need a clone to make a Rasengan. So, to counter Sasuke's Chidori, Naruto made a Rasengan with a single hand for the first time. Later on, Naruto never really noticed how amazing that was, or how he still had to use shadow clones for a while.
In the Fourth Shinobi Great War, after Sasuke and Naruto receive half the Sage of Six Paths Chakra, Naruto has the ability to maintain a perfect Sage Mode, and directly after that, he made a Lava Style: Rasenshuriken with one hand using Four-Tails Chakra and cut Madara in half with it. So he used the sage art Lava Style: Rasenshuriken first with one hand. So it is evident he could make the Rasengan with one hand after gaining the Six Paths power.