The four-man team finished ahead of the German team, who took the silver, and bronze medallists Austria.
The 4x5km relay was won in a time of 48 minutes, 42.2 seconds, with Samppa Lajunen, who claimed the individual title, leading Finland home.
The Finnish team - that also included Jari Mantila, Hannu Manninen and Jaakko Tallus - took a massive 44-second lead after the ski jumping section of the race.
"We had a fantastic ski-jumping competition, but maybe there is more pressure when you are leading," said Lajunen afterwards.
The German team, anchored by Ronny Ackermann, started the relay in fifth place, one minute, 51 behind, but closed the gap to 7.5 seconds on the last lap.
The Austrian team, anchored by World Cup leader Felix Gottwald, finished a further 3.5 seconds behind.
The United States dropped from third after ski jumping to fourth overall, followed by Norway, the defending champions.
Elsewhere, the Russian team, which was due to start ninth after a poor showing in the team ski jumping competition, did not compete after being sent home earlier.
"We had a charter plane leaving Salt Lake City for Moscow and we needed to fill in some empty seats," said Russian Olympic Committee spokesman Gennady Shvets..
"We decided why waste time and money on some athletes who can't compete with the elite."