The 30-year-old carded a 68 to finish at 16 under after 72 holes at TPC Southwind, with Matsuyama and Burns storming through the field on day four with rounds of 63 and 64 respectively.
Matsuyama almost won it on the first trip back up the last as he lipped out from 20 feet but Ancer put his approach to six feet at the second attempt before Burns incredibly got inside him.
Ancer piled on the pressure by making his putt and when Burns missed with his effort, Ancer had his first World Golf Championships win and moved to seventh in the Race to Dubai Rankings in Partnership with Rolex.
American Harris English had entered day four with a two shot lead at 18 under but fired a 73 to finish a shot out of the play-off, one clear of countryman Daniel Berger, England’s Paul Casey and Australian Cameron Smith.
Smith had been in line for a play-off place but a double bogey on the last saw him sign for a 72 and slip back alongside Berger, who finished with a 66, and Casey, who carded a 67.
DeChambeau’s 74 left him at 12 under alongside fellow American Will Zalatoris, a shot clear of England’s Ian Poulter and former World Number One Dustin Johnson.
Abraham Ancer: “I was trying to kind of let it all sink in there in the ceremony on 18. It was really surreal, something that I’ve been working for since I was a little kid. Definitely a dream, a dream come true to win on the PGA TOUR, and to do it on a big stage like a WGC event was really, really cool, man. It was a crazy round. I thought I was going to need a really low one to have a chance today, but it just worked out that it was like pretty much survival mode on the back nine.
“I felt really good the whole week and I’ve been feeling good for a long, long time. I just needed to be patient and just keep putting myself in good positions to win the tournament. Today, obviously the guys had to come back for me to have a chance there with being at 16 under, but like I said before, there’s some tournaments I felt that I played good enough to win and had a great round and things just didn’t go my way and I ended up not winning the tournament. So you’ve got to get lucky times to win events and I’m happy things went my way this week.
“I was probably more nervous of the trophy presentation than in the actual play-off or during the tournament. I felt really calm, I felt like I was ready, I felt like he was there with me. I know he (father) busted his butt his whole life to just get me to tournaments and just have a chance to compete and get better. He definitely would be extremely proud. I know he is extremely proud and having a big old party up there, man.
“I think it’s huge. I know Mexico is in a better spot than some years prior, right now, Mexican golf, but I think it’s getting a lot better. Hopefully this week will inspire some kids to get out there and play golf and learn about the game and just grow the game in general. I’m really pumped where things are headed in my country. Carlos (Ortiz) has been playing some really good golf as well. I feel like we’ve done a really good job. There’s a lot more to come.”
