The Australian started the day three shots behind his play-off rivals at The Renaissance Club but burst into contention thanks to birdie blitz from the third, where he picked up six consecutive shots.
Detry reclaimed the lead at 18 under at the 13th but the Belgian was desperately unlucky as the hooter sounded for a 90 minute delay for thunder and lightning as he was mid-swing for a par putt at the 14th and missed the effort to slip back.
Lee nudged back ahead with a birdie at the 16th, but the final pair followed suit to force a play-off.
The 22-year-old was inches from holing a closing putt for a gain which would have sealed his second European Tour title following his success at the 2020 ISPS Handa Vic Open, but he only needed one extra hole to secure the biggest win of his career.
With victory, Lee also secured one of the three places on offer at next week’s Open Championship at Royal St George’s Golf Club alongside Detry and Englishman Jack Senior.
“It’s an awesome day, I was pretty proud of how I played. Six birdies in a row, that was sweet. It kind of happened really quick,” an emotional Lee said.
“I could have holed a few more putts, in regulation I missed it by a roll, that was painful but we regrouped and the tournament starts in the play-off, pretty much.
“It’s just crazy, I’ve kind of dreamt of it last night and people back home staying up late to watch me, sending messages. This one is for you too.
“I hit a lot of good shots today, that was just one of them. In that situation, it’s a huge moment but I hit so many great shots.
“I’ve been playing really good in recent weeks and just trending, a few mistakes over the whole tournament and wasn’t able to capitalise so it’s awesome to do it here. I’ll enjoy this one.”
Senior, who held the lead after the first two rounds before a 73 on Saturday, made his move during the final round with a blistering start.
The Englishman began his ascend with birdies at the third, fourth, fifth, seventh and ninth to sit alongside overnight leaders Detry and Fitzpatrick before Senior continued his momentum on the back nine.
He dialled into four feet at the tenth and when he rolled in his birdie putt, he was the new leader at 15 under.
Fitzpatrick produced a fine par save on his opening hole to remain one behind, which was matched by Detry from 13 feet but they soon became co-leaders when Senior recorded his first dropped shot at the 12th.
And there was another name in the leadership group. World Number Three Justin Thomas reached the turn in 32 after birdies at the third, fourth, seventh and ninth and he was at 14 under when he rolled in his fifth gain at the 11th.
Senior rolled in another birdie at the 14th to regain the outright lead at 15 under and was joined by Fitzpatrick after he tapped in for one of his own at the third, but the chasing pack applied pressure on the Englishmen.
Thomas increased the group at the summit to three with his sixth birdie of the day at the 14th before Lee made it four in a row at the sixth to also get to 15 under. And then there were a six way tie at the top.
Detry held his nerve to hole successive gains from the fourth to rejoin the leading pack and Poulter decided it was his time to get involved with birdie number six of the final round at the 15th.
There was a new name at the front as Lee took the outright lead after the Australian chipped his eagle effort to concessional range for a tap in birdie to be the first player at 16 under.
Poulter completed a treble of gains at the 16th to sit alongside Lee but the leading Australian’s birdie trail continued with a brilliant 38 footer for six in a row to get himself back in front.
Poulter lipped out at the par three 17th to stay one adrift of Lee and he was joined at 16 under by Detry after his third birdie in four holes at the seventh.
The 45-year-old winner did not go away and he finished Sunday with a birdie to set the clubhouse target at 17 under with his lowest ever final round on the European Tour thanks to a flawless 63.
Following a muted spell at the summit, within a few minutes there was a five way tie for the lead.
Just as Lee narrowly missed a birdie putt at the 13th, Detry and Fitzpatrick rolled in their efforts for a gains at the 11th to get to 17 under, while Ryan Palmer hit the pin as he almost holed out for an eagle at the 16th which would have given him the outright lead.
The American tapped in for his seventh birdie of the day to join the logjam at the top. However, Detry continued his momentum at the 13th.
The Belgian hit a brilliant second from the rough to eight feet and he holed out the birdie putt to lead the tournament at 18 under.
At the next, Fitzpatrick held his par putt to remain at 17 under but as Detry was in mid-swing, the hooter sounded and his effort brushed the left edge, much to his dismay.
He was left with a short putt for bogey on the restart, which he holed, as the leading group returned to a party of five.
But Lee burst clear after his chip at the 16th went inside concessional range for a tap in birdie, his first since the blitz on the front nine, to climb to 18 under, but Detry and Fitzpatrick soon joined him with a gains on the same hole for a three way tie.
The Australian was inches from finishing his round with a birdie which would have sealed his second European Tour title, but he was the clubhouse leader.
The final group could not pick up a shot on the last two holes to secure victory and a three man play-off followed.
But only one extra hole was needed as a clutch approach to 15 feet left Lee with a great birdie opportunity, which he took after Detry and Fitzpatrick could only hole pars.
Poulter and Palmer finished one shot back in a tie for fourth alongside Australia’s Lucas Herbert, who won last week’s Dubai Duty Free Irish Open.
World Number One Jon Rahm finished solo seventh at 16 under, with American pair Thomas and Johannes Veerman one adrift and Senior, who claimed one of the three places on offer for The Open Championship, and World Number Five Xander Schauffele completing the top ten.