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.