The Finn, driving a Skoda Fabia Rally2, inherited the top spot on Saturday morning when early leader Emil Lindholm went off the road during the Kaihuavaara test in his Skoda.
From then on, it was a two-way battle for glory between Asunmaa and Volkswagen Polo challenger Egon Kaur. Stage wins swung from one driver to the other before a time penalty on Saturday afternoon cost Kaur 10sec.
Despite winning both of Sunday’s speed tests, the Estonian was unable to catch back the time dropped with the penalty and eventually ended a mere 4.2sec behind the victor after 251km of flat-out action.
"It's a nice feeling to get my first WRC class win. It was a difficult weekend because normally we run in the top three on national rallies, but the start position is different here and I had to drive with a bit of a different style," Asunmaa said at the finish.
Skoda man Mikko Heikkilä was 1min 34.3sec down on the leading pair in third. He enjoyed a tight tussle with fellow compatriot Eerik Pietarinen, who finished just 6.7sec behind in his similar car.
2016 World Rallycross champion Mattias Ekström completed the top five, 48.6sec further back in another Fabia. The Swede made a rocky start after getting stuck in the snow during shakedown but recovered to enjoy a trouble-free run with Emil Bergkvist alongside.
Estonian youngster Gregor Jeets finished 6min 17.5sec adrift of the leaders in sixth, followed by Pekka Keski-Korsu 2min 32.9sec further back. Keski-Korsu had no room to spare as Tuomas Skantz was just 0.8sec behind in eighth.
Skantz had an even smaller gap to the Citroën of Michal Solowow, who ended an incredible 0.8sec behind in ninth. Johan Kristoffersson completed the top 10, 10min 29.3sec off the leading pace in his Volkswagen Polo.