The entertaining match at the Al Sadd Stadium looked to be heading to penalties after both sides squandered a number of opportunities before Kewell was left unmarked to direct his header home after a beautifully flighted ball from Matt McKay.
Australia, the best FIFA ranked side in the tournament at 26th, will play Uzbekistan in the semi-finals at the Khalifa Stadium on Tuesday.
It will be a first appearance in the last four for the Socceroos, who went out in the quarter-finals on their debut in 2007, and gave their German coach Holger Osieck a win over his compatriot and Iraqi boss Wolfgang Sidka.
"The team showed a lot of heart," Osieck told reporters. "Uzbekistan is waiting. They are a good team and they play a very different game."
Australia created the bulk of chances in the match with Kewell and left winger McKay wasting two good opportunities in the first half when they both struck shots over the bar.
Iraq's playmaker Nashat Akram struggled to find space in the opening stages under the watchful gaze of Australia's midfield duo of Mile Jedinak and Carl Valeri but the holders came back into the game in the second half.
BEST CHANCE
Iraq striker Emad Mohammed spurned the best chance of the match in the 55th minute when put clear after a neat throughball from captain Younus Mahmood but the striker angled his shot wide.
Iraq's Mohammed Kassid continued to be the busier of the two goalkeepers but neither was called upon to make any difficult saves as both sides proved wasteful in attack as half-chances continued to flow.
Australian defender Sasa Ognenovski placed a short-range header directly into the arms of Kassid with Brett Holman warming the goalkeepers hands with a straight drive.
As the match entered extra-time both sides continued to press for a winning goal but Mahmood misjudged his header from close range, Ala'a Abdulzehra's toe-poke lacked power and Jedinak deflected Ognenovski's goal-bound overhead kick over the bar.
With penalties looming Kewell, who had become more ineffectual as the match worn on, chose the perfect time to score his first goal of the tournament.
"Iraq came back very strongly in extra time, I'm particularly happy for Kewell that he got the deciding goal," Osieck said.
Sidka praised his players who looked the stronger side as that match entered its final stages.
"I think we played better in extra time - hard-luck for us, good luck to the Australians - I think it was a very exciting match," Sidka said.
"You saw everything there is to offer in football. The spectators saw a great match. We had many chances, we did everything, in the end it was one cross and one header."
