Almost nothing separated the sides in the first half, with the home side leading 47-46 after two quarters.
However, Jekabpils shot ahead in the third quarter, winning the period 18-11 to take a six-point lead before the deciding part of the game.
Tarvas bounced back and squeezed out a season-opening victory in the last minutes of the game, edging the Latvian opponents by a single point, despite finishing the night with a 36.5% field goal percentage.
Giedrius Gustas, who had seven assists, and Rait Keerles, who collected six rebounds, scored 17 points each for the winners, while Laurynas Mikalauskas added 13.
Troy Barnies was the top scorer for Jekabpils with 16 points and also added 7 rebounds, while Rinalds Sirsnins chipped in with 14 points.