Toyota's Jari-Matti Latvala is third in the team's return after a 17-year absence from the World Rally Championship over two minutes behind rally leader Ogier.
Citroen driver Craig Breen, in last year's older model car, lies fourth in a solid drive - moving up a spot late in the day when Hyundai's Dani Sordo suffered problems.
Ogier felt sorry for Neuville, who deserved better.
"Thierry has driven a great rally, with fantastic speed. To drive the whole of Monte-Carlo in these conditions at that speed is a hard challenge. Monte-Carlo is a rally where you need luck. I wished him no bad luck, he did a great job," said Ogier.
Four special stages remain tonight, including two passes through the iconic Col de Turini stage as well as the power stage, which sees the fastest five drivers pick-up championship bonus points.
Overnight Results
1. Sebastien Ogier (Ford)
2. Ott Tanak (Ford) +47.1s
3. Jari-Matti Latvala (Toyota) +2:20.6s
4. Craig Breen (Citroen) +3:47.3s
5. Dani Sordo (Hyundai) +4:03.2s