The Chicago Marathon takes place on Sunday with the first wave of runners to start at 8:30 a.m.
The 31-year-old clinched a victory over the 26.2 miles to win in 2 hours, 9 minutes and 20 seconds.
Before Sunday, Khalid Khannouchi was the last American victor when he crossed the finish line first in 2002.
As the race progressed in the second half the field began to diminish including world record holder Dennis Kimetto and Emmanuel Bett stepping off the course.
"This is my third marathon and I'm very happy to have won here", Dibaba said. Dibaba was out in front on her own, having gapped Kosgei, while Kirui, Rupp and Ethiopian Sisay Lemma were in contention duking out who would finish where on the men's podium. "It feels tremendous. I feel so great I was able to pull it out".
Ethiopian Tirunesh Dibaba pushed toward a course-record pace nearly from the start to win the women's side of the Marathon in 2:18:31.
Dibaba led at the halfway mark at 1:08:48, well off Radcliffe's record pace, but made another charge that left only Kosgei on her heels. Only Deena Kastor's 2:19:36 at the 2006 London Marathon is the fastest marathon by an American woman.
But ultimately she came up slightly short of the course record. The Kenyan fell back with 10km remaining, leaving Dibaba alone to the end.
She has won several laurels for the East African country at the Olympics and in other worldwide competitions.
Dibaba, 32, is a two-time 5,000m world champion and three-time 10,000m world champion. A year ago in Rio, Dibaba was third in the 10,000 with the fourth-fastest time in history. Rupp was expected to contend after finishing second in April's Boston Marathon with a time of 2:09:58.