The 39-year-old Scot birdied three straight holes on the back nine to hold her third-round lead. She finished at 1-over 71 for a 3-under 285 total.
Im speechless, Matthew said. To be honest, I didnt play that well today but I holed good putts at the 13th and 14th, which I needed. I never imagined coming back ' after not playing ' that I could win. It hasnt sunk in yet.
Defending champion Jiyai Shin never threatened in the final round, and a double bogey at the last hole left her with a 75 and a share of eighth place.
Cristie Kerr and Michelle Wie had their best rounds of the week with 69s. Kerr shared eighth place and Wie tied for 11th.
Matthew birdied from 18 feet at 13 and from 40 feet at the next. She also made a birdie at the long 15th.
When I made that putt on 14, I felt it was mine for the taking, she said. I felt Id never have a better chance and Id better take it. Then once I hit the good tee shot at the 18th, I felt that even I could do it from there.
Creamer dropped two shots on the 18th after driving into a grassy bunker and then sending her third shot past the green and up against the clubhouse.
Disappointing is probably the best word, she said. I gave it a chance. I played really well. Unfortunate luck on the last hole, but I did hit it there so I cant complain too much.
Its all about pride. I wanted to finish as good as I could finish and as close as I could to the top. I wanted to prove to myself I can play a good round on Sunday and I did in a sense.
Wie sufficiently impressed U.S. Solheim Cup captain Beth Daniel to make the team as a wild card. The competition against Europe will be held outside Chicago in three weeks.
Daniel also picked Juli Inkster, who will make her eighth Solheim Cup appearance. Matthew made Europes team after her victory.