Wang birdied the first extra hole at Doha Golf Club after Van Zyl three-putted for par from long range and Lagergren was unable to get up and down from a greenside bunker.
The trio had finished tied on 16 under par after Wang, who won back-to-back events in Morocco and Mauritius last May, left a birdie putt to win inches short on the 72nd hole.
At 21 years and 144 days old, Wang is the third youngest player to win three events on the European Tour after Matteo Manassero and Seve Ballesteros.
He is also the youngest in the world’s top 50 and needs to remain there until the end of March to earn an invite to the year’s first major at Augusta National.
“When I was young, I really wanted to play the Masters,” Wang said. “I always imagined that I would play there. Maybe now I have a chance to play the Masters.
“I’m so happy about it and I hope I’m going to get in the Masters. That’s my dream tournament.”
Wang began the final round with a three-shot lead and birdied the first two holes, but playing partner Van Zyl went one better and also birdied the fifth to close within a shot.
France’s Michael Lorenzo-Vera was the first player to join Wang on 17 under after he eagled the 16th, only to three-putt the 17th from short range and then pull his second shot on the last into the water.
Wang then birdied the 16th to edge ahead of Van Zyl and Lagergren, only to bogey the 17th and then leave his birdie attempt on the last agonisingly short from 20 feet.
“This feels really fantastic for me. It’s really great. I’m so happy,” the 2016 rookie of the year said after a closing 71. “I just don’t want to get any pressure this year. I just want to learn from the other players. I just want to keep winning, I hope.
“I’ve really got a lot of confidence right now, I just want to play another tournament.
“I was really nervous on the back nine,” Wang added. “I missed a lot of greens but my chipping was really good today so I saved everything and finally I won.”
Lorenzo-Vera and South Africa’s Thomas Aiken, who bogeyed the 17th, had to settle for a share of fourth place on 15 under.
England’s Jordan Smith carded a closing 66 to finish a shot further back alongside Spain’s Rafa Cabrera Bello and Nacho Elvira.