The Englishman made three hat-tricks of birdies from the first, sixth and 11th to record his lowest round in a European Tour group event and finish at 22 under, one clear of countryman Wallace, who was also bogey-free in his 67.
The four-time DP World Tour winner hit a wonderful approach into the last to leave himself nine feet to force a play-off but missed on the high side and it was Clements who was left celebrating at Albatross Golf Resort.
Dane Nicolai Højgaard signed for a 69 to finish four shots off the lead, one clear of Scot Robert MacIntyre, who extended his advantage in the race for the third spot on the Ryder Cup team available on the European Points List ahead of next week's final qualifying event at the Omega European Masters.
Swede Ludvig Aberg, German duo Nick Bachem and Maximilian Schmitt, Finn Sami Välimäki and Paraguay's Fabrizio Zanotti were also at 17 under.
Clements won the English Amateur in 2017 but had played events on the MENA Tour before turning professional following the 2018 US Amateur.
He claimed his first professional victories as he won twice on the EuroPro Tour in 2019, the same season he achieved two top-threes on the European Challenge Tour to help earn his playing privileges for 2020.
His big breakthrough came last season, with victory at the Irish Challenge helping him finish 16th on the Road to Mallorca, although he came into this week 151st in the Race to Dubai Rankings in Partnership with Rolex, with a best finish of 21st in 11 made cuts from 21 events.
But he has now jumped 100 places after becoming the first Englishman to lift this trophy in just his 30th Tour appearance.
“Given the circumstances that’s got to be the best round of my life,” a delighted Clements said. “I’m over the moon. I’ve dreamt about winning for a long time and with my birthday coming up on Tuesday I couldn’t be happier.
“Three shots to make up is a tough ask but I knew I was playing well enough to get in amongst it. I feel like I did my job on every shot and obviously the luck was with me today because I holed a few long ones.”
Clements admitted he was inspired by Daniel Brown also winning his maiden title at last week's ISPS HANDA World Invitational presented by AVIV Clinics, adding: “Me and Dan grew up playing golf together, he’s a good friend of mine.
“I was so over the moon to see him win last week, it gave me the belief that I can do it as well. I know I can compete at this level. I’ve always believed it deep down and to show it today I’m very proud of myself.”
Clements started the day three shots off the lead but was soon in a tie as he laid up and left himself 11 feet at the par-five first, played a smart pitch to a foot at the second and holed a 13-footer at the third to get into a share.
Wallace also made his birdie at the first after laying up but Clements holed from 45 feet at the sixth and a 17-footer on the par-three seventh edged him ahead.
He made another birdie on the eighth as he recovered from a poor tee-shot with a stunning recovery to two feet, although he soon saw his lead disappear with Wallace getting up and down from the sand at the front of the green on the short sixth and putting an approach to six feet at the eighth.
Clements then found another gear, holing from 42 feet on the 11th, laying up and putting an approach to eight feet at the par-five next and sticking his tee-shot to four feet at the 13th to lead by three.
Wallace pitched to five feet at the 12th after laying up and then played a beautiful approach to nine feet at the 14th to get within one as Clements made a gutsy seven-footer for par at the 16th and got up and down at the next as he set a target which would prove agonisingly elusive for Wallace.
Højgaard was right in the mix as big drives set up short irons into the second and fourth and he got up and down from the sand on the sixth but he would claim one birdie and one bogey on the back nine as his momentum stalled.
Schmitt held a share of the lead after five birdies in his first seven holes but he faded in a 68, a score matched by Bachem and Zanotti.
Co-overnight leader Välimäki carded a 71, while Aberg and MacIntyre signed for rounds of 66 to finish a shot ahead of German Yannik Paul, who is MacIntyre's closest rival on the European Points List.