The 27-year-old aced the 11th and seventh as he shot a seven-under-par 65 to finish with a two-under-par total of 142, 11 behind leader Matteo Manassero of Italy.
Manassero, 20, winner of last week's PGA Championship at Wentworth, also carded a 65 for 131.
"The shot at the 11th, my second hole, kick-started things," Dodt said. "I made a few more birdies in between, then a couple of bogeys and I was heading the wrong way when I got to the seventh.
"That was an eight-iron, it felt a little bit heavy at the start but it was right on line and went in. I can't get my head around it - I'm pretty proud to be the first one to do it.
"I didn't putt very well today so I'm glad I was able to hole with a long club."
Dodt has one previous European Tour victory to his credit, the 2010 Avantha Masters in India.