Bobby Jones sank two free-throws with five seconds remaining to lift Tercas Teramo to a 77-62 win over Apoel in Italy on Tuesday night.
The margin of victory allowed the hosts to advance to the Eurocup with a one-point aggregate win in the Qualifying Round tie.
Apoel, who won the first leg last week, 77-63, still had time to make a shot that could have put them into the Eurocup and after a timeout, they put the ball in hands of Victor King but he missed from three-point range.
Early in the third quarter, Apoel looked to be in good shape after Ousmane Cissé's basket trimmed the Teramo advantage to 42-40.
Teramo responded by going on a 9-1 run for a 52-41 advantage, only for Apoel to make it 61-56 following a King jump shot.
With 3:42 to play, Ryan Hoover drilled a three-ball that gave Teramo the 15-point lead they needed to win the tie.
Neither side scored again until 2:12 remained when King drilled a jumper.
After Jones and Lewis Hopkins each made two free-throws, Jones drew a foul from Sullivan Phillips and went back to the line to make both attempts from the charity stripe that were good enough to win the tie.
Hopkins finished with a game-high 28 points for Apoel in defeat.
Jones scored a team-high 16 points for Teramo.
Banca Tercas Teramo Coach Andrea Capobianco:
"Our intention was pressing for 40 minutes: it was the only chance to compete in a very intense game.
In the first half we didn't defend as a team, but in the interval we talked about it, and in the second half our defense was really excellent.
Offensively, we made mistakes because of too much impulse, but we are human beings, and we had never played at this level before.
Our supporters drove us in the critical phases, and their assistance was essential to reach this success".
Apoel Coach Christos Stylianidis:
"Congratulations to Teramo, they're a strong team and they won a strong game.
It's very difficult to compete with 27 turnovers and 18 offensive rebounds granted to our opponents.
It was the first time we played in Eurocup, it was a good experience".