On a dramatic final day at The Belfry, the 19-year-old from Denmark came from five strokes back to finish level with Walters on 14 under par.
When the contest went to extra holes, Højgaard held his nerve with consecutive pars down the 18th, with his South African opponent making a bogey on the second trip back down the last after shanking his approach from a bunker.
Højgaard became the first player born in the 21st century to come through Qualifying School last year and soon won in Mauritius, with Matteo Manassero the only other golfer to have captured two titles before turning 20.
“I was a bit surprised that I ended up in a play-off, but it was fun out there,” said Højgaard, whose victory saw him pip Sam Horsfield to the UK Swing Order of Merit.
“It’s hard to describe. It’s obviously an amazing feeling to get the wins. It happened really quick. I’m kind of lost for words right now, but it’s an amazing feeling.”
Højgaard went to the turn in 33 – an approach to within five feet at the sixth the highlight of his three birdies – and added another gain at the tenth.
However, just as he was lurking dangerously on the leaderboard, an errant tee shot on the 11th saw him miss the green and fail to get up and down.
That appeared to leave Walters and Martin Kaymer battling for the title, but in a remarkable finish, Højgaard birdied the 14th and 16th and eagled the par-five 17th to complete a round of 65.
Walters was two shots clear of Kaymer and Benjamin Hebert at the start of the day but, having saved par from a bunker at the first, bogeyed the second after a wild drive finished the wrong side of a thicket of trees.
The 39-year-old South African’s fighting qualities have never been in doubt, however, and he responded with a hat-trick of birdies that took him clear again.
Fellow Dane and ex Ryder Cup captain said of Højgaard, “This young Dane is in for the long haul. Twice a winner at such a young age. Brilliant to watch! Congratulations, a whole nation is proud of you.
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