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, Ivanisevic and Ljubicic broke the Fish serve to love at the start of the fourth set and maintained the advantage to level at two sets apiece after more than two and a half hours of intense play.
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.
