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The Serb second seed now stand two victories away form his dream of finally defending a title in his career after winning the title a year ago.
But Djokovic had to rally from the depths against his Croatian rival, saving break points in the seventh game of the second set to start the reversal of fortunes.
"For a set and half, Ivan was the number two of the world, I couldn't do anything against him," said the relieved seed, who finished up with a break in the last game of the second set to level and swept away the third unhindered.
"Until I began to play better, I had no rhythm, I don't know how I won. I'm just happy to be able to fight and finally get through.
"Ivan was serving rockets, I just had to try and block them back as best I could. In the end I made it."
Djokovic improved to 5-1 against the dangerous 2005 finalist. He will Friday play the winner from while Marcos Baghdatis and German Michael Berrer.
Sixth seed Marin Cilic fell to a rare loss as Jurgen Melzer upset the sixth seed 7-6 (10-8) 7-5 to leave the Croatian with a 17-2 record this season of two titles.
Melzer will play 2007 finalist Mikhail Youzhny after the Russian put out Janko Tipsarevic 6-3 6-4 a day after the Serb defeated Andy Murray.
The victory was a repeat of the emotional Vienna final which hometowner Melzer won over Cilic last October. Cilic claimed their Zagreb semifinal three weeks ago on the way to that trophy.
"When I beat Cilic in Vienna, that was the best day of my tennis life," said Melzer, advancing on his career-best 26th ranking after his performance this week. "But this comes a close second.
"It's been a long time since I've beaten a guy in the Top 10. I played a good match after I changed things up when I was trailing 4-1 in the first set.
"I kept it together. I remembered in Vienna that I changed my game so I tried it again. He was better in our first five games so I had to do something.
"It's very important to beat the good guys if you want to raise your game and raise your ranking. Hopefully there is still more to go." Melzer and number nine Cilic both ended with 11 aces and three double-faults.
