The eight-time world champion started the loop 0.1s adrift but ended with an 18.2s lead after the pair enjoyed a thrilling battle before Lappi's challenge began to unravel in the final two stages.
Hyundai's Thierry Neville maintained third spot, 6.5s behind Lappi, while world champion Kalle Rovanpera headed to service in fourth, 1m03.5s in arrears.
Toyota's Elfyn Evans was forced to nurse his GR Yaris back to the service park after suffering a power loss incurred from damaging his car in a water crossing. Team-mate Takamoto Katsuta and M-Sport's Ott Tanak were also forced to retire from issues incurred from incidents in separate water splashes.
Hyundai's Dani Sordo recovered to sixth after losing three minutes to a crash on Friday, while M-Sport has been forced to retire Pierre-Louis Loubet from the event due to damage to his Ford Puma suffered in yesterday's crash.
Bright skies greeted crews on Saturday morning with no sign of the rain that most feared would impact the schedule.
Ogier pushed in the opening stage of the day (Coiluna-Loelle, 16.28km) but trailed pacesetter Neuville by 1.1s. However, the Frenchman was more importantly 1.8s faster than Lappi to move into a 1.7s overall lead.
The stage featured a particularly challenging water splash two kilometres from the end which caught out Toyota's Katsuta. The Japanese driver damaged the front of his GR Yaris upon impact through the water, which ultimately put him out for the day after a failed attempt to repair the car on the following road section.
Neuville extended his strong start to the day by winning stage nine to edge closer to the battle for the lead which took another twist.
After losing out to Ogier on the previous test, Lappi fought back, taking some risks to claim two seconds out of his rival. It was enough for a sixth lead change of the event as the Finn moved into a 0.3s rally lead.
"That [the lead] doesn't really matter at the moment," said Lappi. "We're just trying to come through the stages with the speed that we have. "There were so many rocks - I managed to avoid most of them but a few I had to drive over. That could cause problems."
Once again water splashes created headlines as Tanak was the next to suffer. The Estonian's Ford Puma ingested a significant amount of water at the hazard, located in sight of the stage end.
The flooded Puma stalled costing the 2019 world champion 20 seconds before he was able to trundle across the finish line using EV mode. The issue prompted a lengthy roadside repair that was in vain.
Evans became the third driver to fall victim to a water crossing when he hit trouble in stage 10. The Welshman suffered damage to the front of his GR Yaris and a power loss after ploughing through muddy water. The Toyota driver managed to reach the stage end with damage to the car's cooling package, but lost 1m53.1s in the process.
At the front, it was the Toyota driven by Ogier that topped the timesheets through the technical test. The four-time Sardinia winner produced a stunning effort to move into a 12.7s overall lead.
A slow puncture on the front left contributed to Lappi finishing 13.0s adrift of Ogier, but the Finn was already 10s down on the split before the tyre issue struck. Neuville was also surprised to slip away from the lead battle after dropping 14.5s in the stage.
Neuville added another stage win in the final test of the loop as Ogier extended his rally lead over a struggling Lappi, who was battling for grip.
"I cannot stop the car from sliding. It is a shame we got a puncture on a good tyre but that's how it is," said Lappi.
Evans was able to drive his wounded GR Yaris through the stage but dropped a further 43.4s.
In WRC2, M-Sport's Adrien Fourmaux moved into a 19.7s lead over Toksport Skoda's Andreas Mikkelsen. The field will complete a second pass through the stages this afternoon.
