Ogier, a six times world champion making a fresh start after leaving Citroen, won the dry opening Malijai-Puimichel stage in the French Alps after the formal start in Monaco.
Belgian Neuville then dominated the icier, 25.49km Bayons-Breziers second stage to lead the rally back to the service at Gap.
"They were tricky conditions. I was trying to read the road as well as I could and not take risks. I think we have done a good time," said Neuville after completing the stage 25.5 seconds faster than Ogier.
Reigning world champion Ott Tanak, who has switched from Toyota to Hyundai, was third overall. (Reporting by Alan Baldwin, editing by Ken Ferris)