Hyundai driver Neuville won only one of Friday's five stages, but the defending rally winner clocked a series of consistent times to lead 2011 Acropolis conqueror Ogier by 2.8s.
Championship and overnight rally leader Kalle Rovanpera managed to limit the damage of starting first on the road to end Friday third, 25.5s adrift, with Toyota title rival Elfyn Evans a further 5.5s back in fourth.
Hyundai’s Esapekka Lappi held fifth ahead of Toyota’s Takamoto Katsuta, with Dani Sordo sitting seventh in the third Hyundai.
M-Sport Ford endured another difficult day that started with Pierre-Louis Loubet retiring from the day’s action before stage two with a suspected water pump issue. Ott Tanak ran as high as fourth before a late departure from a tyre fitting zone prompted a time penalty, dropping the 2019 world champion to ninth.
The morning’s hot, dry weather continued into the afternoon presenting much drier roads than those previously navigated, which featured puddles left by Storm Daniel.
The complexion of the rally changed before the afternoon’s action begun when Tanak suffered a water pump issue during the mid-point tyre fitting zone. It was fixed, but Tanak left the zone 22 minutes late, incurring 3m40s time penalty.
Ogier clocked the fastest time through the afternoon’s first test, stage four, the second pass through Loutraki (10.37km). Officials ultimately cancelled the stage for crowd safety reasons after eight of the nine remaining Rally1 cars completed the route.
The eight-time world champion, competing in a partial season, was 2.2s faster than rally leader Neuville, who managed to increase his overall rally lead to 2.4s.
The stage was held in hot and dry conditions, which proved to be a disadvantage for the early runners. Rovanpera, starting first on the road, dropped to third overall behind Ogier after posting a time 6.0s slower than his Toyota team-mate.
Evans and Lappi shared fourth spot overall, 15.6s shy of the outright pace. Lappi showed improved pace to set the third quickest time on stage four, but the Finn was then forced to pull over on a road section to fix a leaking radiator.
The loop’s second stage featured damp patches, which again played to the advantage of Pirelli’s soft tyres.
Neuville made the most of a gamble to run four softs for the bumpy pass through stage five (Livadia (21.03km), as the Belgian set a blistering benchmark, 5.0s faster than Ogier.
"Tough to make a [tyre] choice before the stage, in the end I said go all in,” said Neuville. "What we can take now will be good for tomorrow, but it wasn't a nice stage to be honest.”
It appeared Neuville would claim a second stage win of the event to date, before a fired up Tanak lit up the timing screens. Benefitting from a better road position following his water pump delay, the Estonian was 5.9s faster than Neuville.
However, Neuville left the stage with headlines as he extended this rally lead to 7.4s over Ogier, who elected to preserve some his soft tyre allocation.
"It was the right choice for there but rally is very long and we don't have that many softs," Ogier said of Neuville's time and full-soft tyre choice. "It's all about strategy.”
Lappi managed to pilot his wounded Hyundai to the fourth fastest time ahead of team-mate Sordo and Katsuta.
Rovanpera bore the brunt of the slippery loose gravel being first car on the road. The Finn was quicker than Evans, but slipped 20.2s behind rally leader Neuville in the overall standings.
Rovanpera continued to suffer in stage six (Elatia, 28.32km), the longest of the day. The Toyota driver dropped 10s but managed to hold onto third overall.
Despite losing the top plane of his GR Yaris' rear wing, Ogier was 4.6s quicker than Neuville's, who suffered a suspected rear differential issue.
Ogier wasn't the only Toyota driver to suffer damage, as team-mate Evans also lost part of his rear wing on his way to the second fastest time that lifted the Welshman from sixth to fourth overall.
The stage was won by Tanak, who claimed his second fastest time of the day.
Yohann Rossel snatched the lead in WRC2 after M-Sport's Adrien Fourmaux stopped in stage six with a puncture.
Six stages await the crews on Saturday.
