Barca edged out Unics 66-63 at home to assume a 2-0 lead in their best-of-five series after holding their composure in a tense finale.
An inspired Nathan Jawai ensured that the visitors remained firmly in contention going into the final minute at 61-61, and the momentum appeared to be with his side.
But Kosta Perovic came up with a big steal and scored crucial points late on to give the hosts a brilliant victory.
Kaith Langford’s desperation shot to win the match was ruled to be after the buzzer, and David Blu stepped up with two clutch triples in the final minutes of the additional time to take the win.
The star performer was rookie Yogev Ohayon, who starred with 15 points and five assists in what proved a stunning display.
Friday’s action sees