Six-times world champion Ogier and his Toyota team mate Evans were tied at the top after the 11th stage but the French driver lost 4.9 seconds to the Welshman in the 12th.
Neuville (Hyundai) won the final two stages on Saturday to end up 1.5 seconds behind Ogier with four stages left on Sunday.
Should he maintain his lead, Evans would win his second rally after prevailing at the 2017 Wales Rally.
World champion Ott Tanak, who was taken to hospital for precautionary checks following a heavy crash on Friday, was released in good health on Saturday.
"I'm good. No injuries, I just stayed overnight. We just hit some bump and I guess we were going a little bit too fast," the Estonian said. (Reporting by Julien Pretot; Editing by Clare Fallon)