The South Korean manufacturer team won the opening Monte Carlo Rally with Thierry Neuville, who was fourth on Sunday.
Lappi and co-driver Janne Ferm, competing in their first rally of a part-time season, finished 29.6 seconds clear of Toyota's Elfyn Evans with M-Sport Ford's Adrien Fourmaux on the podium for the first time.
Frenchman Fourmaux had been second until he hit a snowbank on Sunday morning.
Briton Evans took seven points for leading the Sunday classification under a new scoring system, while Toyota's double world champion Kalle Rovanpera, another part-timer this year, took five bonus points from the final stage.