The 23-year-old LIV Golf talent burst three strokes clear after consecutive birdies on the second, third and fourth holes to shoot five under on Sunday and finish at 18 under, two ahead of China's Wenyi Ding.
The final round began with 31 players jostling within six shots of the lead.
But the steady Spaniard (68, 67, 65, 66) - he leaked just two bogeys, back-to-back in the second round, all tournament - made the first move and then had all the answers to claim the record $450,000 prize.
He is just the ninth international winner of the event in nearly 100 years and second since 1998.
Puig followed in the footsteps of legendary countryman Ballesteros, who came from five shots back to win by three from Billy Dunk with Greg Norman tied for third at Royal Melbourne - the host of this week's Australian Open - in 1981.
Ballesteros, a five-time major winner, former world No.1 and Ryder Cup great, was 24 at the time and had already claimed the Masters and British Open when he went one better than his runner-up finish a year earlier.
"My name, being with Seve's name as the only two (Spaniards) … makes it even more special," he said of the European golf powerhouse who died in 2011.
"I never saw him play in person, which sucks to be honest.
"I watched replays of every major he won and all he did.
"He's such a big figure for Spanish golf. His presence and everything he accomplished; it's marked in Spanish players and in a way we try to be like him.
"Play with that freedom ... attitude, behaviour and how much he cared and hopefully we're kind of on the right path."
The Arizona State standout left university early to join the rebel LIV tour in 2022 but has played sporadically in Europe's DP World Tour and the majors for the last two years.
Prior to the Brisbane event he committed as a full member to the 2026 European tour, happy to balance his schedule and accept any sanctions that come his way.
Marc Leishman (15 under, tied third) and Min Woo Lee (14 under, tied fifth) both got within two shots after the turn as they shot 67 and 69 respectively on Sunday.
But their slip-ups on the testing 14th hole, and a classy Puig birdie on the 13th and ice-cold par on the next, gave him a comfortable buffer down the stretch even after Ding (66) birdied the 16th and 17th.
Adam Scott (69) finished seventh at 13 under, left to lament a string of near misses for birdie early in his round that kept him at arm's length from the leaders.
New Zealander Nick Voke (66) made a late run to finish in a tie for third with Leishman, while countryman Daniel Hillier (14 under) had four back-nine birdies to share fifth with Lee.
Leishman, now boasting three-straight thirds and a 2018 runner-up finish at the event, threatened all week but remains without a major Australian trophy on his resume.
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