Law, who had started the final day a shot off the lead along with compatriot Scott Jamieson, covered the last four holes at Green Eagle Golf Courses in two-under for a closing 73.
The battling one-over effort for a three-under 213 total saw the 30-year-old Aberdonian finish in a tie for seventh - his best effort on the circuit since winning the ISPS Handa Vic Open in February 2019.
While Law had another victory in his sights heading out at the start of the day, his performance on a course regarded as one of the toughest on the European Tour will be a huge confidence boost for the rest of the season.
Playing in the same group as the two-time Scottish Amateur champion, Jamieson holed a 20-foot birdie putt on the opening hole to move into a tie for the lead.
However, the 37-year-old Glaswegian’s card contained six bogeys thereafter as he signed off with a 75 as he had to settle for a tie for 18th on one-under alongside Connor Syme (71).
In an event that saw all seven Scots in the field make the cut, Richie Ramsay (70) finished joint-25th on par, one ahead of Callum Hill (73) as he came up short in his bid to secure a spot in next week’s US Open at Torrey Pines.
Ten places were up for grabs in the season’s third major through a mini-order of merit taking in three European Tour events and those spots went to Richard Bland, Guido Migliozzi, Bernd Wiesberger, Armitage, Mikko Korhonen, Jordan Smith, Adrian Meronk, Edoardo Molinari, Dave Coupland, Thomas Detry and Matthew Southgate.
Armitage joined Betfred British Masters winner Bland and Made in HimmerLand victor Wiesberger in securing his trip to California in style as the 33-year-old made his breakthrough thanks to a closing 65.
Helped by a sensational effort that included an eagle and six birdies, Armitage finished on eight-under, one ahead of fellow Englishman Southgate, who had a chance to force a play-off until he drove into the water on the last.
The win came in Armitage’s 71st appearance on the circuit and the man known as ‘The Bullet’ admitted it was an emotional occasion after losing his mother, Jean, to cancer as a teenager.
“I’ve dreamt about this since that day, being a winner,” he said. “You have times when you think it might not happen. I just stuck at it. Today is a great day, I’m sure she’d be proud.
“This one’s for me. Deep down, it’s for me. All those lonely days on my own, dealing with life. All those lonely days working at my dream. I’ve got to take a lot of credit for it myself.”
Huddersfield-based Armitage hadn’t fancied himself to win this event, adding: “It’s funny because in the practice round I’ve never lost as many golf balls in a practice round in my life.
“I’m not a massive fan of the course, and I thought I’d miss the cut this week and go home a bit disappointed.”
David Drysdale (75) and Stephen Gallacher (76) finished on three-over and seven-over respectively.