The 19-year-old from Florida, who was tied in the lead on 10-under with fellow American Michelle Wie after the third round, recorded an impressive bogey-free 68 in the final round to finish 14-under-par at Mission Hills Country Club.
Thompson dropped just three shots all weekend and claimed four birdies on the front nine in her flawless fourth round to take the title with Wie three shots further back after carding a final-round 71.
She admitted she was "honoured" with her victory: "It was an amazing day. Starting off with a birdie definitely helped. But just hitting that first tee shot obviously a little nervous, but it was definitely what I've been practising for, what I live for, to play under that pressure and to get a major win under my belt, especially the Kraft Nabisco. It's such a huge honour to win this tournament."
English teenager Charley Hull, who was tied for third following a six-under-par 66 in the third round on Saturday, dropped off the pace and finished in a three-way tie for seventh after carding a disappointing final- round 76 which included a double bogey on the eighth hole, three bogeys and a birdie.
Scotland's Catriona Matthew was two shots further back, finishing two-under-par for the tournament.