Campillo looked on course for a two-stroke victory on the final day of the tournament but a wayward tee shot on the par-4 17th gave him a double bogey that meant he finished tied on 13-under overall.
In the ensuing playoff, Campillo sank birdies from 20 feet and 25 feet. On their fifth extra hole, he sank another exceptional 20-foot birdie while Drysdale missed his putt to hand Campillo his second European Tour title.
"I'm just so proud right now of the way I played in the playoff," Campillo said. "I hardly missed a shot and I was able to make some putts.
"I hit some good shots coming in, in the middle of the round. But you have to be patient, you have to try hard. I knew I was going to make some putts. It was a tough win but I'm glad I pulled it off.
"It's a great par four, 18. A tough hole. David was hitting some great shots into the hole and I had to make some putts. Three birdies out of six on 18 to win is something to be proud of."
The event was Drysdale's 498th on the European Tour and the 44-year-old is yet to win a title, finishing runner-up four times.
The Scotsman had his chance to clinch the title on the 18th but he missed a birdie putt by mere centimetres which forced the playoff.