Tartu Rock reached the EuroCup Final Four last season but they made an early exit from the competition in 2008-09 after losing in the Qualifying Round 1 to Basket Swans.
After falling 86-64 in Austria, the Estonians returned home and prevailed 75-60 on Tuesday, leaving them with a 146-139 defeat on aggregate.
Deteri Mayes had 23 points to lead Basket Swans, and after the contest he received a great compliment from his coach, Bob Gonnen.
"We won because we have the best player in Austrian basketball history, Deteri Mayes, who shows excellent play in important games," Gonnen said.
"Also our point guard (Anthony Paul) Fisher had an excellent performance in the second half and that led us to victory."
No lead is safe against a team from the Baltics and that was apparent at the end of the first quarter when Tartu Rock had outscored Basket Swans 28-12 to trail by just six points on aggregate.
After Sten Sokk's two free throws at the end of the second quarter, Rock had taken a 48-25 lead - a one-point advantage over the two legs.
Twice Rock went in front by 27 points in the third quarter, the second time at 60-33 after Tanoka Beard's jump shot midway through the third quarter.
Basket Swans held the home side to just two points for the rest of the quarter and Fisher's three-pointer cut the deficit in the game to 62-42, leaving the Austrians ahead by two over the two legs.
Mayes then scored 14 of his points in the fourth quarter as Tartu Rock held on.
"We won the series because we were the better basketball team in the fourth quarter in both matches," Mayes said.
"We just kept fighting and we never gave up - that brought us to the second round."
Georgia international George Tsintsadze of Tartu Rock, a EuroCup all-star last season, said: "Our opponents scored well from difficult positions in the fourth quarter and we had no strength to fight to the end."
Head Coach Bob Gonnen (Allianz Swans):
"We won because we have the best player in Austrian basketball history - Deteri Mayes, who shows excellent play in important matches. Also our point guard Fisher showed excellent performance on second half and that lead us to victory."
Player Deteri Mayes (Allianz Swans):
"We won the series because we were the better basketball team in the fourth quarter in both matches. We just kept fighting and we never give up - that brought us to the second round."
Head Coach Üllar Kerde (Tartu Rock):
"Our attack in the second half didn't run as it should and our opponent had two men who won the match for Swans. We worked hard to take a 27-points lead but had not enough strength to hold it."
Player George Tsintsadze (Tartu Rock):
"Our opponents scored well from difficult positions on fourth quarter and we had no strength to fight to the end."