Lawrence had a five-shot lead early on the back nine at Blair Atholl Golf & Equestrian Estate but was reeled in by his playing partner before getting over the line by one stroke at 16 under par.
At the presentation ceremony – after dropping the trophy off its base and catching it one-handed – Lawrence said: “This is what you strive for, being a kid you dream for this moment, to win such a prestigious event in front of an amazing crowd.”
Sweden’s Jens Fahrbring finished third on his own at 14 under after a closing 70.
Sordet made the perfect start, with birdie at the first while Lawrence's bogey wiped out his two-shot overnight lead.
But the reigning Sir Henry Cotton Rookie of the Year regained the initiative as a wonderful approach to the fourth set up birdie - and a three-shot swing as the Frenchman made a double-bogey six.
Lawrence made a good two-putt from long range to match Sordet's birdie at the next and though Sordet pulled one back at the seventh, he bogeyed the ninth while Lawrence made birdie to take a four-shot advantage to the turn.
He extended that at the next before both players dropped a shot at the 12th – as did nearest pursuers Fahrbring and Wilco Nienaber. The latter’s push for a top-five finish was ended by a nine at the next.
Sordet birdied the 14th and when Lawrence’s par putt slid just past, the lead was down to three with a dramatic finish back on the agenda.
Lawrence found water down the left of the next and could only pitch up from a path for double bogey.
Sordet was in deep rough next to a greenside bunker but got up and down for par to take a further two out of the lead – and it was all square with two to play after Lawrence bogeyed the next.
A short miss for Sordet led to a bogey at the 17th, though, and he found a bunker off the last tee.
Lawrence was safely in the middle of the fairway and a fine approach, combined with only a par for Sordet, meant he could even afford a three-putt from the fringe of the green for the title.
Lawrence said: “It felt all easy going through the round and then golf happened at the end.
“Clement was playing really well, I was playing well then made a few mistakes, missed them on the wrong sides and couldn’t score from there.
“I managed to get it done and I’m really pleased.”
On the mishap at the 15th hole, he added: “Me and my caddie got the wind wrong but the mistake’s on me, I still need to hit the golf shot – I took a conservative line and I shouldn’t have, I’ve been aggressive all week.
“It was unfortunate for Clement on 17 to miss that short one - it’s just golf.
“I want to cry, I’ve got no words.”
Fahrbring, the final member of the lead group, went out in 33 with three birdies and one bogey – an identical tally to Lawrence to effectively end his chances of eating into the South African’s huge lead. Two birdies in the last three holes saw him finish on the heels of Sordet.
Matti Schmid finished fourth on 11 under, helped by his fifth eagle of a remarkable week with a putt of over 70 feet at the fifth - which was followed three holes later by his fourth double bogey.
Fellow German Marcel Siem surged into the top five with a bogey-free outward nine of 31 and saved par with a good putt at the 13th, but a shot out of bounds at the 14th led to a double bogey before his par putt at the next horseshoed out.
Siem finished in a group at 10 under alongside Dean Burmester, Chase Hanna and Daniel Brown.
South Africa's Christian Maas won the Freddie Tait Cup as the leading amateur at five under.