He was still trailing by three shots on the 16th tee but a birdie on that hole, followed by a stunning eagle at the last, where his approach finished eight feet away, piled the pressure on Ormsby, who cracked with a double bogey on 17. "It's not something I expected".
"At the beginning, I was just super nervous, stressed and anxious, and I kept missing cuts", says the 25-year-old, only the second Duke graduate to win on the LPGA Tour (joining Brittany Lang), and the fourth golfer from France (but first since 2003).
Had Ormsby been able to match Law's eagle on the final hole, he would have forced a playoff, but he could only manage a birdie.
France's Celine Boutier won the women's event by two shots from three players including England's Charlotte Thomas.
The victory represents a remarkable turnaround on the course for Law, who was on the brink of taking on other work over the winter before winning last season's SSE Scottish Hydro Challenge and finishing 14th on the Challenge Tour to earn a European Tour card.
It was co-sanctioned this year by the European Tour and US LPGA Tour for the first time.
Ormsby chipped in on the fifth to pull a shot back and gained another on the ninth to get back to par for the round before gains on the 13th and 18th holes gave him the outright lead.
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If the Sweden global is passed fit he is likely to start against the French champions at Old Trafford on Tuesday night. He is a Manchester United player.
"I've been loving the four events I've played so far and to just be a European Tour player was what I was happy with".
Law said: "To have won, it sort of changes things a little bit". Yeah, I'll go home, reflect a little bit on things and reassess.
Scotsman David Law, South African Justin Harding and Australia's Brad Kennedy were then three shots off the lead in a tie for third place.
Kemp opened her round with a double bogey but struck nine birdies to finish strong, unlike overnight leader Kim Kaufman, who blew a two-stroke lead with a disappointing six-over 78 and finished in a tie for eighth place.
"Until then, it was just about trying to get into position for a top-three or a top-two finish".
"We stood on the tee and we said we need to make eagle", Law said at the trophy presentation after claiming a A$1.5 million ($1.06 million) winner's cheque. "We make eagle, we post at 18 under, you never know what can happen".
He tweeted: "The work we do @paullawriefound is not to raise golfers to win on tour but when one of our kids does win on tour which happened today it's an awesome feeling".