Only 10 other players have won at least five majors -- Inkster won the Dinah Shore again in 1989 -- and all of them are in the Hall of Fame.
"I can't comprehend this," said Inkster, who turned 39 the day of the first round. "It's been an awesome year. For once in my life, I'm speechless."
Inkster finished at 16-under 268, by five strokes the lowest 72-hole score ever recorded at Dupont in the six years it has been host of the LPGA Championship.
Nancy Scranton, tied with Inkster with three holes to play, and Mardi Lunn of Australia tied for third at 273. Defending champion Se Ri Pak shot an even-par 71 and finished seven strokes back.
It was the second straight year someone has swept the LPGA Championship and the U.S. Open, the two oldest majors in women's golf. Pak won both last year, becoming the first rookie to win two majors since Inkster won the Dinah and du Maurier in 1984.
For Inkster, it was her 17th consecutive round under par during a streak that began the last week of April and carried her to the Grand Slam.