Gillman, the 16-year-old Austin, Texas, player who has committed to Alabama, had a 5-under 66 for an 11-stroke victory. She had a 16-under 268 total to break the tournament record of 271 set by Aree Song in 1999.
After opening with rounds of 66, 66 and 70, she took a six-stroke lead into the finale.
''I tried not to change my game plan in the final round even though I had the big lead,'' Gillman said. ''I wanted to keep making a lot of birdies and not make many mistakes. I'm actually still in shock I won. It hasn't all sunk in quite yet.''
The 18-year-old Burns, a future LSU player from Shreveport, Louisiana, took the lead with a 65 in the completion of the suspended third round and closed with a 71 for a two-stroke victory. He finished at 10-under 274.
Gillman earned a spot next year in the Swinging Skirts LPGA Classic in California, and Burns qualified for the PGA Tour's Texas Open.
Last year, Gillman shared the 54-hole lead and ended up tying for third.
''I went to the final hole one back last year and I still felt like there were some shots I left on the golf course, which would have given me a chance to win or at least get me in a playoff,'' Gillman said. ''I wanted to get revenge this year.''
Burns built his lead to six strokes on the front nine, with birdies on the par-5 first and the par-4 eighth. However, he made consecutive bogeys at Nos. 12 and 13, shrinking his lead to one stroke. But a string of five straight pars to finish was enough for Burns to claim the title.
''I started hot on the front nine with a few key birdies,'' Burns said. ''I hit a tough stretch, but I was ultimately able to keep it together and it feels so good.''
Burns also won the AJGA's Tournament of Champions this summer.
''I'm really speechless and incredibly honored to have had the success I've had this summer,'' Burns said. ''If you would have told me at the beginning of the summer I'd be in this position, I wouldn't have believed you.''
Bethany Wu of Diamond Bar, Calif., was second in the girls' division. She finished with a 70.
Gordon Neale of Trabuco Canyon, California, was second in the boys' division. He had a 73 in the third round and a 67 in the fourth.
Gillman, Burns, Wu and Neale also secured spots on the U.S. Junior Ryder Cup team that will face Europe in Sept. 22-23 at Blairgowrie in Scotland.