Unicaja reach the Final Four for the first time in their history winning the best-of-three series 2-1, denying 2003 champions Barcelona a second-straight trip to the last four.
Malaga point guard Pepe Sanchez drained the game-winning three-pointer with 7.7 seconds left in the match to put the hosts up 65-62.
After a quick foul against Barca point guard Juan Carlos Navarro, the Spain international hit a pair of free throws then the visitors fouled straight away.
But Marcus Brown iced the game from the line to give Unicaja a 67-64 lead, and Malaga fouled Jaka Lakovic immediately to prevent a three-point attempt by the visitors.
Lakovic missed both and Barcelona failed to collect the rebound handing the victory to the hosts.
The win in the final stretch cemented a fourth-quarter recovery by Malaga after the hosts relinquished the lead they had maintained throughout the second and third quarter.
After Barca went up by five points with four minutes left to play, Unicaja coach Sergio Scariolo called a timeout and the hosts fought back to tie the game at 56 thanks to a one-handed bounce pass from Sanchez to Jiri Welsch for an easy layup.
Scariolo praised his side's pre-match preparation and on-the-court performance.
"In 25 years as a coach I never saw a team that prepared so well and hard tactically for a game, as my guys did these three days. We managed to overcome a big blow to our team as was Dani Santiago's absence," Scariolo said.
Santiago, Unicaja's center, had to miss Thursday's match after undergoing an emergency eye operation and will be out for six to eight weeks.
In Santiago's absence Marko Tusek had a big-game leading all scorers with 15 points.
Sanchez, a member of the Spanish world championship winning team, added 11 for the eventual victors including the crucial three-pointer.
Big-man Fran Vazquez led Barca with 12 points, as Navarro was only able to score a disappointing 9 points.
Barcelona coach Dusko Ivanovic sounded a note of frustration after opting to sit out Vazquez in the final minutes and watching his side fail to put up a three-point attempt that could have tied the game.
"Unicaja was not really superior tonight but they won the game, just as we could have won it," Ivanovic said.
"It was my decision to sit Fran Vazquez for the last minutes. In these cases you can always win or lose and we got the worst part today."
Follow LIVE coverage of the Final Four in Athens starting May 4 on www.eurosport.com.