The championship's scoring system has changed this year, with the leader on Saturday - Neuville - banking 18 points providing he finishes on Sunday.
Ogier, chasing a record-extending 10th Monte Carlo win on home roads in the French Alps, is assured of 15 while Toyota's third-placed Elfyn Evans - now 34.9 seconds off the lead after being ahead on Thursday and Friday - gets 13.
A maximum of 12 more points are available on Sunday, five of them for winning the final Power Stage.
Belgian Neuville went from third overnight to first by the lunchtime service point, 5.1 seconds clear of Evans who had hybrid power problems, after winning two of the three morning stages.
France's eight-time world rally champion Ogier replied with back-to-back stage wins to take the lead in the afternoon before Neuville clinched the closer and went back ahead.
"It was perfection," said the Hyundai driver. "Everything went well and I really enjoyed the car. It was incredible.
"It was important to take the points tonight but we also needed to keep the car on the road. I had a good feeling, so I went for it and it seems like it paid off."
Toyota's reigning champion Kalle Rovanpera is absent from the opening round as part of the Finn's decision to run only a part-time programme this year, leaving Evans as the team's main title contender.
"It’s not been the best day for us. The morning was a bit mixed: the first stage was difficult to judge with a lot of black ice, and then in the middle stage we didn’t have the hybrid power, which was not ideal," said the Welshman.
Ogier is also doing only a partial season but still adding to his collection of records and wins.
Victory on the day's penultimate Les Nonieres-Chichilianne stage was the 700th of his career, putting him fourth on the championship's all-time list of stage winners.
Hyundai's Ott Tanak won the 11th stage and ended the day fourth overall but a minute and 46 seconds behind Neuville.
The Rally ends with a prize-giving ceremony in Monaco's Casino Square on Sunday after the final blast over the Col de Turini.
