Ogier, bidding to overhaul team-mate Jari-Matti Latvala at the top of the World Rally Championship, charged to victory on both the 30-kilometre Ibarrilla and 53km Otates stages to hold a 49-second lead heading into the midday service.
Latvala is now his nearest challenger, inheriting second after Mads Ostberg hit a bank on SS12 and broke the left-rear upright on his Citroen DS3.
He attempted to fix the problem before the mammoth Otates run, but missed the stage start after stopping on the road course and failed to begin SS13 before the 30-minute time period.
That, allied to a strong pair of stages, elevated Neuville to third, the Belgian delivering the Hyundai i20 WRC's most convincing performance of its debut season to leapfrog Elfyn Evans.
M-Sport's Welshman is still within touching distance of the podium though, excelling on the tricky rally so far and keeping calm on the two long runs to end the morning 11.1s behind Neuville.
Team-mate Robert Kubica struggled though, and was one of two drivers - the other being Andreas Mikkelsen - to end SS13 upside down after rolling his Fiesta (pictured) for the second time in two days.
As on Friday, Martin Prokop and home favourite Benito Guerra continued without serious drama to benefit from the issues of others and complete the top six.
Chris Atkinson and WRC 2 leader Yuri Protasov had problems - the former had to run first on the road while the latter had no power steering on Otates - but reached service without incident to hold seventh and eighth.
Mikko Hirvonen and Kris Meeke, despite running under Rally 2 regulations after their Friday woes, complete the top 10.
Leading positions after SS13:
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- Sports & Recreation
- Mads Ostberg
- World Rally Championship
- Jari-Matti Latvala