Team mate and reigning champion Ott Tanak retired after going off with steering failure in the morning's opening stage, but will rejoin on Sunday.
Belgian Neuville meanwhile won three of the six stages to end the day with a 33.2 second advantage over Frenchman Sebastien Loeb.
Nine-time world champion Loeb, 46, had on Friday become the oldest driver to lead a world championship rally and won Saturday's closing stage after getting his tyre choice wrong for the morning loop.
The Frenchman ended the second leg level with Toyota's championship leader and compatriot Sebastien Ogier, who had been slowed earlier by a puncture and hydraulic problem, but ahead on a tie-break.
"We worked on the set-up and I was happier with the car in the rough sections. But nothing is done," said Neuville.
"Tomorrow has the roughest stage of the rally and we need to avoid punctures and damage on the car, but we still need to drive fast."
Sunday is a long final day with four stages totalling 88.86km and ending in the Marmaris Wolf Power Stage with bonus points for the fastest five. (Reporting by Alan Baldwin in London, editing by Ian Chadband)