That result has hauled him up to third in the World Rally Driver's Championship, equal with his vastly more experienced team-mate Jari-Matti Latvala.
Together with Ott Tanak, they gained enough points to be just one point behind Hyundai in the World Rally Manufacturer's Championship after two of the 13 rounds to be held this year.
"Today we were able to show some good performance by winning all three stages," said Team Principal Tommi Makinen.
All three drivers suffered from their high start places last Friday when they were forced to clear snow off the forestry roads after fresh overnight falls. They lost time to the later starters who had better conditions.
In his first start in a winter rally in a WRC car, Lappi was the most impressive as he rebounded up the leader board.
"To get the Power Stage win and gain two places today has been very good," said Lappi. "I'm really happy for the team as well, at least we got some kind of good result from this weekend. I wasn't expecting this kind of speed from my side."
Jari Matti Latvala said: "We lost so much time on the first day with our high starting position in the fresh snow and the heavy ruts. We changed the transmission for the final day. The team did a very good job and the car was handling very well. It is both quick and reliable and that is important."
FINAL RESULT, RALLY SWEDEN
1, Thierry Neuville/Nicolas Gilsoul (Hyundai i20 Coupe WRC) 2h52m.13.1s;
2, Craig Breen/Scott Martin (Citroen C3 WRC) +19.8s;
3, Andreas Mikkelsen/Anders Jaeger (Hyundai i20 Coupe WRC) +28.3s;
4, Esapekka Lappi/Janne Ferm (Toyota Yaris WRC) +45.8s;
5, Hayden Paddon/Sebastian Marshall (Hyundai i20 Coupe WRC) +54.4s;
6, Mads Østberg/Torstein Eriksen (Citroen C3 WRC) +1m15.3s;
7, Jari-Matti Latvala/Miikka Anttila (Toyota Yaris WRC) +2m04.9s;
8, Teemu Suninen/Mikko Markkula (Ford Fiesta WRC) +2m52.2s;
9, Ott Tänak/Martin Järveoja (Toyota Yaris WRC) +3m44.4s;
10, Elfyn Evans/Daniel Barritt (Ford Fiesta WRC) +5m27.4s.
Manufacturer's championship points:
1, Hyundai 54;
2, Toyota, 53;
3, Citroen, 46;
4, Ford, 43.
Driver's championship points:
1, Neuville, 41;
2, Sébastien Ogier (Ford Fiesta WRC) 31;
3=, Lappi, Latvala, 23;
5=, Tanak, Mikkelsen, 21.