Thomas, who had waited for more than half an hour after a closing eagle to start the playoff, hit first and was long on the 17th hole.
Reigning Masters champion Garcia fired a bogey-free 65 that included a 22-foot eagle putt at the par-5 11th and a 16-foot birdie at 18 to grab a share of second place.
It's been another year of exciting performances at the World Golf Championship Mexico Championship. "He hit a attractive tee shot on one, you can tell he can really play", Mickelson said.
Phil Mickelson finally looked like the Lefty of old Sunday in the Mexico Championship, especially when a final round of pressure, possibilities and dramatic shots that kept the crowd buzzing finally ended at Chapultepec Golf Club.
"Then he just realised and said, "So sorry, I thought you were media".
Defending champion Dustin Johnson was a shot further back on 10 under. He added, "I made a few mistakes on the greens but the greens are tough this week so I think everyone's making a few mistakes".
Phil Mickelson has broken through for his first victory in more than four years, beating Justin Thomas in a playoff to win the World Golf Championships-Mexico tournament. A victory in the World Golf Championship would be his third title in his last eight starts, and likely put him in the top 25. "I enjoy that. That's what was so fun".
Sharma's WGC debut comes after European Tour wins last December at the Joburg Open and last month in Malaysia at the Maybank Championship. Playing alongside Hatton and Mickelson Sunday, Sharma struggled to find the form that helped him lead through three rounds.
"Man, there's nothing for me to hang my head about", Thomas said.
"I love that nervous feeling that you get when you're in contention, I just haven't felt it that often", he said.
Sharma, who lives in Chandigarh though his family hails from the northern Indian state of Jammu and Kashmir, is the country's highest-ranked golfer at No. 66.
"To me, he has a very calm attitude. I remember when he made that putt to get into the playoff, I jumped on my bed and nearly broke it". I know he's a very talented player and I believe he's leading the Order of Merit on the European Tour, so I know what a great player Mr. Sharma is.
That put him two clear of five-time Major victor Phil Mickelson (65), reigning Masters champion Sergio Garcia (69), Englishman Tyrrell Hatton (64) and Spaniard Rafa Cabrera Bello (69).