The Latvian win was powered by strong offensive rebounding and the sharp-shooting of Karklina.
Leading scorer Lyndra Weaver was held to five points on two of 13 shooting, but on the offensive side, Vilnius couldn't overcome 19 turnovers.
The Lithuanians also struggled behind the arc, hitting just 14%, but had a chance to tie the game with 30 seconds left.
Lindsey Marcie Harding's three-ball was off the mark, however.
Milka Bjelica led Vilnius with 16 points and 14 rebounds.
Lisa Willis had a fine all-around game for Riga, finishing with 17 points and seven boards.
Riga will look to finish the season with consecutive wins, facing UMMC Ekaterinburg next Wednesday, while Vilnius will travel to Italy to play Cras Basket Taranto.
Quanitra Hollingsworth, TEO Vilnius:
"We came out ready to win but in the end we didn`t finish our job. We were outrebounded, however we cannot use this as an excuse."
Kristīne Kārkliņa, TTT Riga:
"We did not start as well as we should. After the Christmas break we worked hard to improve our physical condition, maybe that`s the reason why we were slow in the beginning. We had a lot of missed shots, we lost the rebounds. But we improved our performance and in the end we won. We are highly motivated for every game in the EuroLeague Women. Now we must try to win in Ekaterinburg."
Aigars Nerips, TTT Riga coach:
"We played aggressive, we played emotionally and achieved our goal. This was our last home game, it was important to win. We are happy to win this game and look forward to continue on the same note."