The 19-year-old Thompson beat Wie into Poppie's Pond, too, capping the breakthrough major victory with the traditional victory leap into the water near the 18th green. ''It's just a dream come true,'' Thompson said.
Thompson closed with a bogey-free 4-under 68 for a three-stroke victory. She birdied four of the first nine holes to open a five-stroke lead and parred the final nine.
''This is what I've worked so hard for,'' Thompson said. ''This was one of my goals coming into the year, to win a major. I've always seen myself winning a Kraft Nabisco. It's such a huge honor with all the history behind the tournament.''
Wie was second, birdieing the final hole for a 71. She used her driver only four times, choosing to hit fairway-metal stingers on the other 10 driving holes - leaving her as much as 60 yards behind Thompson. When both hit 3-woods, Thompson also had the advantage.
''I stuck with my game plan and I think it was the right play,'' Wie said. ''Who knows? In hindsight you would do something here or do something there, make a putt there. That's the way golf is. I just couldn't get anything going today.''
Thompson finished at 14-under 274 for her fourth LPGA Tour victory. She opened with a 73, shot a tournament-best 64 on Friday and had a 69 on Saturday to tie for the lead with Wie at 10 under. The 6-foot Florida player had only one bogey - when she missed a 3-footer on the par-5 18th Saturday - in her last 55 holes.
''You have to hit it in the fairway and, if you miss it, just miss it small,'' Thompson said. ''I think just staying into it mentally. When I had a bad hole, I'd just fight right back. Or if I hit a bad shot, just know that I can get it up-and-down or get it on the green.''
Thompson won the 2011 Navistar LPGA in Alabama at 16 to become the youngest winner in tour history, a mark broken by Lydia Ko in the 2012 Canadian Women's Open. Last year, Thompson won the LPGA Malaysia and Lorena Ochoa Invitational.
The 24-year-old Wie made her 12th start in the event. She was ninth in 2003 at age 13, fourth the following year and tied for third at 16 in 2006. She also was sixth in 2011.
''I thought I played OK,'' Wie said. ''I think it just got to a point where I just tried to force it. I think I needed to really come back with a lot of birdies and I think it got to a point where I just tried too hard. But I'm just proud of myself for how the week went.''
Wie has two tour victories, winning the 2009 Lorena Ochoa Invitational and 2010 Canadian Women's Open. She has been in the top 16 in all six of her starts this season.
Thompson hammered a drive 40 yards past Wie's 3-wood on the par-4 opening hole and took the lead with a 15-foot birdie putt. Wie pulled even with a birdie on the par-5 second, chipping to 1 1/2 feet after leaving her second shot just short of the green.
Wie bogeyed the par-4 third, missing from 6 feet after a short chip.
Thompson birdied Nos. 4 and 5. She hit a 3-wood 30 yards past Wie's 3-wood and made a 12-foot putt on the par-4 fourth, and holed a 5-footer on the par-3 fifth.
Thompson picked up another stroke on the par-3 eighth when Wie missed a 2-foot par putt, and pushed her lead to five with an 8-foot birdie putt on the par-5 ninth.
Wie birdied the first two holes where she used her driver, hitting it past Thompson on the par-5 second and 11th. Wie also hit driver on the par-4 13th, setting up a wedge that she hit to 4 feet. But she left the birdie putt short to remain four strokes back.
She cut it to three on No. 14, holing a 12-footer, but dropped a stroke on the 17th.
''Lexi played amazing today,'' Wie said. ''She played probably the best I've ever seen her play. She hit the ball so well. She made everything. It was just hard to catch up to her all day today. I'm really happy for her. I'm really proud of her.''
Stacy Lewis, the 2011 winner, had a 67 to finish third at 7 under.
DIVOTS: Minjee Lee, the 17-year-old Australian who tops the amateur ranking and is 110th overall, was the low amateur. She shot a 72 to tie for 24th at even par. Lee won the Australian professional tour's Victorian Open in February. ... Inbee Park, the 2013 champion, had a 75 to tie for 38th at 4 over.