The New Zealander carded a remarkable closing 64 in the high winds and set the clubhouse target with an eagle to apply some pressure to Lee down the stretch.
A bogey on the 17th meant the 21-year-old only took a one shot lead down the last but he birdied the par five as sister and two time champion at 13th Beach Club Minjee looked on.
The elder sibling won the women's event as an amateur in 2014 and lifted the trophy again as part of the paid ranks in 2018, with Min Woo now adding a chapter to a remarkable family legacy in Geelong.
"My sister and I winning the same tournament, it's pretty special," he said. "I've got bragging rights now so it's even better."
Minjee added: "I was super, super proud of him. It was really cool to just even be here with him and even watch him the last two holes. Just to see him play, I haven't really seen him play that much, so to be able to have a win here is really cool."
Minjee finished two shots out of a play-off at six under in the women's event this time around as Hee Young Park lifted the trophy.
Lee announced himself on the European Tour two years ago this week when he made the quarter-finals of the ISPS Handa World Super 6 Perth as an amateur.
After making his professional and Rolex Series debut at the following season's Abu Dhabi HSBC Championship presented by EGA, Lee achieved back to back top fives but narrowly missed out on keeping his playing privileges in his rookie campaign.
He recorded a best European Tour finish as he finished third at the Australian PGA Championship just before Christmas, but is now in the winner's circle in just his 19th event.
"It's awesome," he said. "Vic Open, it's the home open. Especially as it's the European Tour, it's big. I'm over the moon.
"I thought coming in I had a really good chance because I was hitting it really good but I think I impressed myself with the game this whole week.
"I felt really comfortable just because if I did exactly the same as yesterday, I felt pretty hard to stop. I started off really hot off the gate and it was pretty comfortable those last few holes. It got a bit nervy but I'm pretty proud of the way I finished."
Lee made a stunning start with his chip-in for birdie on the first but the lead remained at three as Fraser put an approach to six feet.
The par five second was proving gettable and the leading duo both took advantage, with Lee getting up and down and Fraser two putting from off the green after hitting the pin with his second.
Lee almost drove the green at the par four fourth and got up and down to extend his lead to four shots but Fraser trimmed it back to three as he picked up a shot on the par five next.
Fox made his birdie on the second and then drove right up to the side of the green on the fourth, holing a long putt for eagle in a big early move.
A tee shot to eight feet at the par three seventh handed him another birdie and he holed a ten foot right to lefter on the tenth to get to 14 under.
A 12 footer on the 16th had Fox in a share of second and when Fraser failed to get up and down on the 14th, he was there alone.
The 33-year-old was still three back but he put his second on the last to four feet for an eagle and set the clubhouse target at 17 under, putting Lee under real pressure for the first time all day.
The leader responded in perfect fashion, breaking a run of ten pars by driving right up to the front on the par four 15th and leaving himself a tap-in for birdie.
He failed to get up and down on the 17th but put his second to 12 feet on the last to seal victory.
Fraser bogeyed the 17th but picked the shot back up on the last to sit in a share of third alongside Smyth, who also carded a 70, and Sciot-Siegrist who signed for a 68.