The 18-year-old Thompson made a 5-foot putt on the par-5 18th, then won when Lewis missed her 5-foot try.
''First off, I had like a 50- to 60-footer for the first one, which was interesting getting up there within a few feet,'' Thompson said. ''You know on the second putt, that's what it all came down to thinking I can make it and went up to it confidently. Just knock it in.''
The third-ranked Lewis, a three-time winner this year, had a 68.
''I knew I had to make it,'' Lewis said about her birdie try on the final hole. ''I had a good line on it, just with these greens, those downhill putts are the hardest ones to make. I hit a good putt. I hit it where I wanted to. It just didn't go in.''
Thompson closed with a 3-under 69 to finish at 16-under 272 at Guadalajara Country Club. She won the 2011 LPGA Navistar Classic at 16, and took the LPGA Malaysia last month for her second tour title.
So Yeon Ryu was third at 13 under after a 69.
Top-ranked Inbee Park finished fourth at 11 under to wrap up the points-based player of the year award with one event left. She is the first South Korean player to win the award.
''I said all year, there should have been at least two or three girls that already won the award, but nobody really did it,'' said Park, who shot 69. ''It's just really hard to believe and I'm just very lucky I won.''
Lewis birdied Nos. 12-14 to take a one-stroke lead, but dropped into a tie with Thompson with a bogey on the par-3 17th.
''Stacy is an amazing player,'' Thompson said. ''I knew she could make a run at me any time during that round. When she made the two-shot swing on me, I think on No. 12, it brought it back to all squared. I knew I had to make birdies on top of her because she gets on a roll and she doesn't stop. She's an amazing player and played great today.''