Lee went into the final round with a three-shot lead and the 21-year-old showed no signs of nerve as he carded a four-under-par 68 to finish with a winning aggregate of 19-under 269.
“I started off really hot off the gate and it was pretty comfortable those last few holes,” Lee, who began with a birdie on the first, said afterwards.
He bogeyed the 17th to take a single shot lead down the last and birdied the par-five as sister and two-time champion of the women’s event Minjee looked on.
“It was nice of her to come on...my sister and I winning the same tournament, it’s pretty special. I’ve got bragging rights now, so it’s even better,” he said.
New Zealander Fox carded a closing 64 in the high winds to put pressure on Lee down the stretch but could not deny the Australian his breakthrough victory.
Marcus Fraser and fellow Australian Travis Smyth joined Frenchman Robin Sciot-Siegrist at 14 under, two shots clear of another Australian in Jake McLeod.
Minjee, who won the women’s title in 2014 and 2018, could not make Sunday’s playoff and finished two shots behind the leading Korean trio of Hye-Jin Choi, Hee Young Park, and So Yeon Ryu who were locked at 281.
Reporting by Amlan Chakraborty in New Delhi; editing by Simon Cameron-Moore