In buoyant mood after a 4-2 away win to begin the series, KooKoo backed that up with a 3-2 success at home in game two, but they finally came up against a more resilient version of the top seeds on the return to Tampere.
A fairly quiet opening period with five shots on goal apiece came alive in the 17th minute, albeit with a touch of good fortune. Joni Tuulola worked the puck across for Kasper Simontaival to hit, and his strike would have gone wide had it not deflected in off Oiva Keskinen, who didn't know much about it.
Tappara's discipline had an impact on their victory, as they didn't concede a powerplay throughout the match. KooKoo had Jesper Alhlroth called for slashing soon after the opening goal and Eetu Randelin penalised for tripping in period two, neither of which the home side could utilise.
The second period was when KooKoo stepped up in search of an equaliser, but despite nine shots on goal to Tappara's three, they failed to find a way past Christian Heljanko, who thwarted some of the better chances that fell to Vilmos Gallo and Robert Rooba.
Heljnko managed to keep out another 12 efforts on goal in the third period, taking the total for his shutout to 26, as high-sticking from Oskari Luoto six minutes from time didn't help the visitors at the business end of the match.
Although, they were back to full strength when the Battle Axe finally secured the win - Jyrki Jokipakka lifted the puck high from behind his own net, sending it sailing over all the KooKoo heads before it dropped down and into the net for a spectacular empty-net goal.
The 2-0 victory gets Tappara on the board and means they will welcome KooKoo back to Nokia Arena for game five on 9th May, but first, they head to Kouvola for game four on 8th May.