The reigning world champion, who was third after Friday's opening leg on the rough gravel roads around Lamia, led by more than two minutes from Hyundai's Dani Sordo (40).
Belgian Neuville had led overnight and was 10.9 seconds clear when he shattered his Hyundai's front-right suspension on a pothole at the start of the afternoon loop of stages.
Eight-time world champion Ogier then led and was 12.4 seconds clear of teammate Rovanpera going into the day's final stage when he smashed into a rock and broke his Toyota's rear-left suspension.
“There was a lot happening at the front today,” said Rovanpera. "It was a nice battle of course, but not the easiest to push with Seb because we had the championship to think about.
"I think we had a good day, we were fast but we also kept the car in one piece."
Rovanpera started the weekend with a 25-point lead over teammate Elfyn Evans (34), with Neuville a further 11 behind, but is set to stretch that advantage after the Welshman ended the day third overall.
Sunday features 43.3km of timed stages with up to five bonus points available in the final stage.
The Acropolis Rally is the 10th round of the 13 race championship.
