The 27-year-old birdied the second playoff hole to beat England's Joe Dean and Sweden's Marcus Kinhult after all three were tied at 11 under on Sunday.
All three birdied the first extra hole, the par-5 18th, but Migliozzi was the only player able to repeat the feat after making a hole-in-two and two-putting long on the green.
Kinhult's chances were effectively gone when he hit his second shot into the water around the green, and Dean missed a 20-foot birdie opportunity when he mishit his tee shot and couldn't reach the green in two.
Dean, a former delivery driver, was relieved to have secured two places for next month's British Open at Royal Troon alongside Migliozzi, with Dean's higher world ranking enabling him to qualify ahead of Kinhult.
Migliozzi had previously had four bogeys in the six holes starting from the 9th hole, but he made birdies on the 16th and 18th holes to finish the final round with a score of 70 and enter the play-off. Dean also made a birdie on the last hole, with a total of 30 strokes on the back nine holes, chasing Kim Holt.
“It was a great battle,” said Migliozzi, who bogeyed the 10th hole because he couldn't find his pristine tee shot in the three minutes allowed.
“After I lost the ball on 10, I thought to myself 'If I can get through this, I can do this'. I never thought I was going to be done. I always try to make birdies and come back and now here I am. It's an incredible feeling.
“It’s great to be here now.”
Finland's Mikko Korhonen led Migliozzi by one stroke going into the final round but finished with a 75 and tied for 10th.
Denmark's Rasmus Hojgaard and Italy's Andrea Pavan both lost by one stroke outside the play-offs, with Pavan setting an early clubhouse target with a fine 65.
Kick-off was delayed by two hours on Sunday as Extinction Rebellion activists blocked the entrance to the International Court.
The first eight teams had already set off, but the rest were pushed back, with the leading group finally setting off at 3pm local time.
Australian Andrew Martin (73) and Thomas Power Horan (70) both finished one stroke over, and they tied for 51st with their partners.
© Golf Australia. All rights reserved.
