After being thoroughly outplayed for the first two sets, Ivanisevic, weakened by an arm injury and playing his first top-level match since shoulder surgery last May, somehow lifted his game and the Croatian pair snatched the third set on a tiebreak, winning it 7-5.
Roared on by an intimidating crowd in Hall Dom Sportiva,
The deciding set with serve until the ninth game, when Blake was unable to make a low volley from Ivanisevic's attempted pass. Ljubicic then served out to give a jubilant Croatia team an incredible victory.
Ljubicic will meet Blake in the first of the reverse singles on Sunday, while 18-year-old Mario Ancic is scheduled to play Fish in the final match of the tie.