Neuville started the day 3.0s adrift of Evans with the gap increasing to 6.5s after a strong morning loop from the Toyota driver.
However, a charging Neuville turned the tables across the afternoon stages to move into a 4.0s advantage heading into Sunday.
Hyundai’s Ott Tanak headed to service in third (39.9s) having inherited the position after world champion Kalle Rovanpera dropped almost three minutes to a puncture after a run in with a rock face during the morning’s first stage.
Toyota’s Takamoto Katsuta ended the day in fourth (1m04.5s) ahead of his eight-time world champion teammate Sebastien Ogier, who lost almost three minutes to a puncture on Friday.
M-Sport’s Gus Greensmith held sixth spot, with Rovanpera sitting in 11th after a day of drama.
The intense fight for the victory between Evans and Neuville continued into the afternoon stages with the latter stepping up his charge.
While its was Ogier that set the pace on Stage 11, Neuville was only a 0.1s adrift, but more importantly was 2.6s faster than leader Evans, who had set the pace in the morning pass through Nukata Forest (20.56km).
It meant Evans’ overall lead was reduced to 3.9s, while Ogier moved ahead of Greensmith, who battled an intermittent power steering issue on his Ford Puma.
Tanak was unable to match the front runners as he continued to struggle in finding the sweet spot in his i20 N. The Estonian was 0.6s faster than Katsuta as the pair fought over third overall.
Rovanpera was surprisingly off the pace during the stage as the world champion dropped 31.6s, which he attributed to trying new set ups given he had nothing to fight for after this morning’s puncture.
Stage 12 proved to be a key moment of the rally as a charging Neuville assumed the rally lead from Evans.
The Belgian navigated through the 14.74km Lake Mikawako test, 5.9s faster than Evans despite fighting a spinning differential.
"It was actually not a very good run,” said Neuville. “I did a good stage but I had some real trouble with the diff spin. Luckily it was the last proper stage of the day.”
Evans dropped two seconds behind Neuville in the fight for the victory after battling with the handling of his GR Yaris.
"There wasn't a lot left but it wasn't a good run either I've lost the feeling with the front of the car a bit this afternoon," said Evans.
The sister Toyota driven by Rovanpera also continued to struggle running an experimental set up, as the Finn posted the slowest Rally1 time for the second consecutive stage.
"We found some things which work but definitely on this stage it's not working,” said Rovanpera. "In the beginning of the stage I could not do much more with the car and I am not on a crazy place, so of course we are not so fast.”
There was some positive news for Toyota as Ogier, also testing a different set-up, chalked up his fourth stage win of the event to date.
Stage 13, a first pass of the Okazaki City super special, was delayed for almost an hour due to the late arrival of safety crew. Two passes of the 1.40km stage were planned but due to the delay, organisers elected to cancel one of the passes.
Action eventually resumed in front of thousands of spectators that lined the stage that featured sections of tarmac and sandy gravel.
Neuville further extended his lead after winning the final stage, talking two seconds out of Evans in the process.
In WRC2, Emil Lindholm remained on course to secure the title with the Finn leading his class by 47.6s.
Rally Japan will conclude on Sunday after a further five stages, comprising 69.82 kilometres.
