Matthew led by one shot after an opening 67 and by two after a second-round 71, and her closing 71 for a 209 total sealed the win by a shot from Norway's world No.6, Suzann Pettersen (69). England's Laura Davies snatched third place on three under following a 68.
Carly Booth, the Scottish Ladies' Open and Swiss Open champion, had been joint second going into the final 18 holes, but posted a 76 to drop back into a tie for seventh on 216, level par. But it was still another fine result for the 20-year-old Scot from Comrie.
But Matthew, ranked No.27 in the world, proved that she is still the Scottish No.1. She has now won four European and four US LPGA titles, plus the 1996 Australian Open and the British Open. On a great weekend at London 2012, the 42-year-old Scot relished the prospect of staying at the top of the game in time for golf's re-entry to the Olympic Games in Brazil in 2016. "Playing in the Olympic Games would certainly be a great addition to my career," she said after collecting the £44,000 winner's cheque.