The teams were all even after the first quarter, with the scoreboard showing 18-18 after the first ten minutes of play, but the hosts broke away in the second quarter.
Parnu jumped ahead to a 35-29 halftime lead after winning a 7-0 run to close out the second quarter after Nemanja Miljkovic made a basket with a couple of seconds left in the half.
However, Barsy responded with a run of their own in the third period, winning an 8-0 stretch to turn a six-point deficit into a 45-43 lead halfway through the quarter.
Although the visitors started the final period with a two-point lead, Parnu bounced back and took an upper hand at 58-53 after a bucket by Janis Vahter with five minutes remaining.
The teams were still even with a minute left in the game, but Gytis Sirutavicius scored two points to give Barsy a 63-61 lead, but Zivojin Grubovic responded with a long-range shot.
The lead changed hands a few more times, before Janis Vahter went one-of-two from the free-throw line to knot things up at 67-67 with eight seconds remaining.
However, in the last possession Mikhail Yevstigneev managed to find Lithuanian big man Edgaras Zelionis, who drained the game-winning shot with only a second to spare.
Zelionis was the only Barsy player in double digits with a game-high 25 points and added eight rebounds to his total, with fellow Lithuanian Gytis Sirutavicius adding nine points.
21 points and seven boards from Janis Vahter fell short of bringing the home side the win, as Nemanja Miljkovic added 14 points for Parnu.