After falling behind by as many as 16 points midway through the second quarter, Tartu battled back and made sure of a thrilling finish in the Group G game.
Three times they closed the gap to four, the last at 74-70 with 34 seconds remaining on a Tanel Sokk three-ball.
Folarin Campbell answered with two free-throws for Artland, but Janar Talts gave Tartu hope again by sinking another three-pointer to cut the deficit to 76-73 with 26 seconds to go.
Tartu fouled Campbell again and he drilled two more before Ronald Ross added a pair for an 80-73 Artland advantage with 14 seconds to go.
The Estonian team refused to go away.
Silver Leppik nailed a three-pointer for Tartu to make it 80-76 and the hosts quickly fouled Campbell with 11 seconds remaining.
Campbell, a perfect 12 of 12 on the season before Tuesday, had made five of six on the night as he went back to the line.
He was off target on both attempts, but Tartu failed to take advantage as Talts grabbed the rebound and then threw the ball away.
Tartu fouled Toby Bailey and the veteran sank one of two attempts for the five-point triumph.
Tartu dropped to 1-4 with the defeat and fell out of contention for a place in the Last 16.
Campbell scored a season-high 22 points the Dragons with Darren Fenn contributing 16.
Talts ended up with 20 points and eight boards in defeat.
Indrek Visnapuu, Tartu University/Rock coach:
"Little things made all the difference tonight. In the first quarter we were leading 11-2 and then we gave away our initiative and could not recover. We still had our chances in the last minutes, but Dragons played a good game and deserved to win."