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.
Source: Autosport