Firing a rousing pre-Masters warning, Lee held off golf's biggest names Scottie Scheffler and Rory McIlroy to secure a steely one-shot victory in a pulsating finish at Memorial Park Golf Club.
World No.1 Scheffler, the second-ranked McIlroy and a swag of other heavyweights stormed home to threaten to crash the in-form Australian's party.
After extending his four-shot third-round advantage to five at one point, Lee's buffer was slashed to one down the stretch after he found the water off the tee on the par-5 16th and Scheffler, like only he can, reeled off four successive birdies.
But the Perth prodigy recovered from his first bogey in 41 holes to par the last two to secure the biggest win of his life and complete an extraordinary family double.
His scrambling par at the 72nd hole, from 54 feet and off the green to inside a foot, symbolised the 26-year-old's grit on championship Sunday.
Lee eventually closed with a three-under-par 67 to post a tournament total of 20-under 260.
Scheffler finished with a typically-sizzling 63 to share second with fellow American and former US Open champion Gary Woodland.
Woodland had set the clubhouse lead at 19 under with a tournament-record-equalling 62, a brilliant round matched by big Finn Sami Valimaki, who was outright fourth at 17 under.
After starting the day eight shots back, McIlroy had to settle for joint fifth at 15 under after conjuring an eagle and six birdies in a round of 64.
But the day and the spoils belonged to Lee, who was stoic and scintillating in equal measures as he warmed up beautifully for the Masters, the year's first major starting at Augusta National in 11 days' time.
"It's unbelievable," he said after following his LPGA Tour star and dual major-winning sister Minjee as a professional champion in the US.
"It was a big mental grind and I'm very proud. Looking around, the Houston crowd was awesome obviously and (Texas home favourite) Scotty was there and it was nerve-wracking."
Lee looked to have slammed the door shut on his chasers with back-to-back birdies on the 12th and 13th holes to surge four shots clear of Scheffler, before potential disaster struck on No.16.
He had to reload off the tee after failing to carry the water, but escaped with a hugely important bogey to prevent a three-shot swing and retain the lead.
Lee's breakthrough, which follows two PGA Tour runner-up showings, three DP World Tour victories including the 2021 Scottish Open and 2023 Australian PGA, comes a fortnight after he let a halfway share of the lead slip at the prestigious Players Championship.
The newly-crowned champ paid credit to his experienced caddy, Shane Lowry's 2019 British Open-winning bagman Bo Martin, after the Irishman played a huge part in the turning point of the final round.
Martin had to talk Australia's social media superstar out of attempting an audacious shot off his knees on the par-5 eighth hole.
Struggling with his driver all round, the West Australian was fortunate to stay in bounds but still found his ball under a tree.
After a lengthy deliberation, he wisely opted to take a two-club-length penalty drop and eventually saved par after a painstaking 33-minute drama.
"He did a great job," Australia's new No.1 and world No.22 said of Martin.
"You lean on your caddy a lot and we knew we could win one day.
"I've been playing a lot of good golf the last couple of months so to get it done, yeah, him and I knew it was going to happen.
"But it was exhausting, and it's tough winning out here, so I want to do it more.
"I've got to gear up for it. Let's keep it rolling."
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