Adrian Banks buried a game-winning jump shot with three seconds remaining to lift Belgacom Liege to a 73-72 triumph at CSU Asesoft Ploiesti.
Ploiesti led by as many as 12 points but lost by one for the second consecutive week with poor free-throw shooting their undoing.
They missed 12 of their 26 attempts for a woeful 57.1%.
The home team will agonize over the final minute of this game.
After Banks' shot, the hosts called a timeout and tried to come up with a winning play.
The Romanian club ended up with a chance to snatch victory at the death but Kevin Burleson's shot was off target.
Ploiesti, who fell 74-73 at Enisey Krasnoyarsk in their opener last week, were in very good shape early in the second half.
They had their biggest lead at 51-39 after a lay-up by 35-year-old center Rashard Griffith.
Later in the third quarter, however, Guy Muya's three-point play triggered a 9-0 Liege run that put the visitors in front at 57-55.
Ploiesti went back in front in the fourth quarter and looked to be headed for victory with 29 seconds left after a pair of free-throws by Adrian Blidaru gave them a 72-68 lead.
Following a three-point play by Belgacom's Will Thomas to reduce the deficit to 72-71, the Belgians fouled Griffith and the American missed both free-throws.
Muya capitalized with his game-winning shot.
Liege were 13 of 17 at the charity stripe.
Romania international Catalin Burlacu finished with 21 points and seven rebounds in defeat while Banks had 19 in the victory.
Thomas had 17 points and nine rebounds for Belgacom, who bounced back from last week's 79-74 home defeat to BC Donetsk.
Gjergja Dario, Belgacom Liege head coach:
"I am very happy about the win; I think we've deserved it. We are a very young team and our goal for this year is to accumulate as much experience as we can. I think is going to be difficult for all the teams to qualify from this group, because of the trip to Siberia, but also for Krasnoyarsk, who has still to play in Romania and Belgium."
Adrian Banks, Belgacom Liege player:
"I still don't know how the last shot got in, but I'm glad we won. Asesoft had a very aggressive defense and we had a very hard game."
Vladimir Arnautovic, CSU Asesoft Ploiesti head coach:
"I take the entire responsibility for this loss. I shouldn't have left Rashard Griffith on the court in the last possession. Everybody knows he can't shoot free throws, but I thought that he would make a good block. My players did a great game; they've respected everything we've talked about before the match.
"Anyway, I still think we have some chances to qualify but we have to be perfect."
Catalin Burlacu, CSU Asesoft Ploiesti player:
"I can't believe we've lost by just one point. It's the second game in a row. We did a good job today, but we couldn't concentrate at the end. It's a shame, the crowd was great today and since it was Romania's National day today and we wanted to celebrate."