Avenida (5-2), who joined Beretta-Famila Schio at the top of EuroLeague Women Group B with the triumph, trailed 64-58 early in the fourth quarter but held their nerve.
Le'Coe Willingham scored to start a 9-0 run that was capped by two Sancho Lyttle free-throws.
The Salamanca club went in front by six only for the Croatians to twice knot the contest in the last 1:36, the last at 79-79 after two free-throws by Carla Thomas.
After Lyttle, who had 24 points and 15 rebounds, missed with a jump shot, Andja Jelavic tried to put the Croatians on top but she was off target with a jumper.
Avenida regained possession and Anke De Mondt missed a three-pointer only for Gorbunova to haul in the rebound and score on the put-back to clinch victory.
Willingham scored 19 points and Spain's exciting youngster, Alba Torrens, poured in 14 for Avenida.
Thomas finished with 24 points and six boards for Gospic, who fell to 1-6 with the defeat.
Jordi Fernández, coach Halcón Avenida:
"It was a complicated and hard game but we were lucky in the last secondsd with Gorbunova's offensive rebound and the made shot. We defended their three scorers better in the second half. We are very happy for the victory."
Isabel Sanchez, player Halcon Avenida:
"We know that it is necessary to fight until the last second. Today's game simply demostrated that all the teams are dangerous."
Stepe Bralic, coach Gospic:
"To lose two games in the last minute is a bit harsh. We need to improve our situation play in the closing minutes. I am satisfied with the team's overall performance."
Andja Jelavic, player Gospic:
"We are proud of our hard job on the court, but this is not enough when you lose the game. We will try to win our second EuroLeague game next week."