In a battle of two sides that managed just one victory in their eight Division A games last year, hosts Finland threatened to blow out Mark Clark's Brits in the first half.
Reetta Piipari's three-point play gave the home side a 27-13 advantage at the end of the first quarter.
Kimberly Butler responded with a basket for Great Britain as the visitors clawed their way back in the second quarter to trail 36-30.
Taru Tuukkanen took her points haul to 12 with a jump shot three seconds before half-time to give Finland a 43-36 lead.
British center Sarah McKay, however, who also had 12 points in the first half, set the tone for the third quarter with a jumper.
That basket sparked a 12-0 run that was capped by a three-ball from Kristy Lavin.
Lavin, who missed all of last year's games with a ruptured anterior cruciate ligament, would go on to hit three shots from the arc on her way to 10 points in more than 17 minutes of action.
Finland never recovered from their slow start to the third period and trailed the rest of the way, although they did stay within striking distance.
Tiina Sten's lay-up cut the deficit to 63-61 with 1:43 remaining and they had two more chances to tie the game but Piipari and Sten each missed lay-up attempts.
Butler finished with 17 points and seven rebounds to lead Britain, who also got 15 and six from McKay.
Sten paced Finland with 13 points and seven boards.
"It was good for us to face one of the favourites of this group right in the beginning of our campaign. Despite of the loss I saw many positive things in the game. I am proud of the way we came back after a difficult third period. We have the best possible players available for us and I believe we will improve game by game. Therefore I feel confident going for our away games."
Reetta Piipari, player, Finland:
"We had an excellent start in the game, but made some bad shooting choices later on. Great Britain play very aggressive defense and it caused us big difficulties, especially during the second half of the game."
Mark Clark, Head Coach, Great Britain:
"I am very pleased with the win after having such a short preparation period. I am also pleased with the way we handled the great start by Finns. We didn't panic, kept our focus on our game plan. It was an important victory for us since I see Finland as one of the strongest teams in the group."
Lisa Hutchinson, player, Great Britain:
"We were very nervous in the beginning. But we knew what to do, did it and it paid off. Our defense won the game for us today."