England's Tom Lewis (65) made a spirited charge, but after making five birdies in his first five holes, he ran out of steam and finished third at 264.
Australia's Min Woo Lee, younger brother of LPGA Tour star Minjee Lee, shot a second successive round of seven-under par 63 in only his second start as a professional to finish solo fourth, one shot behind Lewis. Frenchman Alex Levy (65) was fifth on 266.
"It feels really good. Any time you can win a professional golf tournament, no matter where it is in the world, it's a big win. I'm honoured to be the champion, and I'm very pleased," said Johnson. "I'm heading back to the States tonight, and I've got three big weeks in a row. I've got Pebble Beach, LA and Mexico coming up. To win here, obviously the game is in good form."