They won the first set 15-13 but then the RAF took the second 15-.11 to draw level in the best of five sets.
Riga trailed at one stage In the third set but hit back to score a 17-15 win in a crucial part of the match.
It was another hard fought affair in the fourth set with Riga again trailing but they ran out 15-13 winners.
"It was one of our toughest matches ever and we were on court for nearly two hours - our longest spell of the season," said Riga spokesman Tom 0jasoo.
"Although we won by two clear sets the match was a lot closer than the scoreline suggests," he added.
