The Spaniard held a two shot lead with two holes to play but a double bogey on the 17th dropped him back to 13 under and we went to extra holes for the second week in a row.
Campillo found sand off the tee on the first trip back up the last but a 25 foot putt brought a birdie which Drysdale matched from six feet.
A 20 footer brought another birdie for the 33-year-old and with Drysdale even closer to the hole than after his previous effort, the duo shared a fist bump before returning to the tee after another pair of birdies.
Both men made routine pars on the third and fourth play-off holes and were given a buggy to make their way down the fairway as the light began to fade in Doha.
Another putt from beyond 20 feet brought Campillo a birdie and when Drysdale missed from similar range, Campillo was a two time winner in his 250th event after five extra trips up the last.
Campillo had to wait 229 events for his first European Tour victory at the Trophée Hassan II but he has now won in consecutive seasons.
"I'm just so proud right now of the way I played in the play-off," he 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."
For Drysdale, this was the 498th European Tour event without a win and a fourth runner up finish.
There was a two shot swing on the very first hole as Winther put his approach to ten feet and Campillo made a bogey.
The overnight leader was back in a share of top spot as he took advantage of the par five second from six feet, with Drysdale playing a beautiful bunker shot to save par on the fourth.
The 44-year-old took advantage with a birdie from ten feet on the next to make it a three way tie, as Winther missed a golden birdie opportunity from six feet.
He would make no mistake on the seventh and after putting another approach in tight, he was at the top on his own.
Campillo put an approach to tap-in range on the tenth and when Winther failed to get up and down from the sand on the 12th, Campillo was the solo leader.
He got up and down at the par five 13th to lead by two and despite having to play out sideways and dropping a shot on the 16th, he stayed two ahead as Winther three putted from just off the green.
Drysdale had missed a very short putt on the eighth to drop back to 13 under but he put an approach to eight feet on the 14th before bogeying the next as he failed to get up and down.
But he soon found himself in a share of the lead as Campillo went a long way right off the 17th tee and three putted from just off the green for that double bogey.
Winther also three putted from just off the green and Campillo and Drysdale made their closing pars to set up the play-off drama.
Lemke made birdies on the second, fourth, fifth, sixth, eighth, 11th, 13th and 14th to surge up the leaderboard but made two late bogeys in a 65, while Samooja holed very long putts on the ninth and 11th in a 69 containing four birdies and two bogeys.