Kärpät left winger Mika Pyörälä nailed down the victory, putting Oulu ahead 2-0 early in the third period, assisted by Jari Viuhkola.
That 2-0 lead proved too much for the host Helsinki team to overcome. The Oulu defence, led by goalie Niklas Bäckström, effectively kept the Jokerit at bay.
Jokerit won on Friday in Oulu to keep their hopes alive after losing the first two games of the best-of-five series. They went into Sunday's game in Helsinki hanging by a thread, down by two games to one.
Hopes of a come-from-behind series win began to fade as Kärpät embarrassed the host team by getting on the scoreboard first -- during a Jokerit power play, no less. Petr Tenkrat, one of Oulu's three Czech stars, slipped the puck in past Jokerit goalie Tim Thomas, a veteran of the Boston Bruins.
Kärpät won both away games during the finals, leaving little doubt of their supremacy.
The title is the third for Kärpät, established in 1946 in northern Finland's biggest city. Before last year, their only previous win dates back to 1981. This was the team's fifth appearance in the finals. They lost to Tappara of Tampere in the 1987 and 2003 finals, and had to settle for silver. The team also has four bronze medals.
Jokerit is the only other team to score back-to-back Finnish championships, winning the title in 1996 and '97. However Turku's TPS and Tampere's Tappara have both won triple consecutive titles.