The 21-year-old Hingis stretched for a backhand passing shot in the third game of the match but her feet fell out from under her and she fell on her back. After dropping that game to go down 2-1, she had her ankle tapped but was forced to stop two points later.
Hingis, the No. 1 player for 209 weeks, needed to defeat Davenport to remain on top for a 74th consecutive week. She also was looking to win her third straigt Porsche Tennis Grand Prix title and fifth overall.
The Swiss star remains winless in her last 13 tournaments--the longest drought of her career.
Capriati becomes the ninth player to attain the No. 1 position since the inception of the computer rankings in 1975, and the fourth from the United States.
Her rise to the top of the rankings caps a remarkable comeback. The 29-year-old Capriati, who left the tour for two years during the mid-1990s due to highly publicized personal problems, won her first Grand Slam crown in January at Australia and claimed a second major in Paris. She also was a semifinalist at Wimbledon and the U.S. Open.
Davenport, the 1998 champion, improved to 14-10 lifetime against Hingis and advanced to her eighth final of the year.
In Sunday's final, she will take on sixth seed Justine Henin of Belgium, who posted a 6-3, 7-6 (7-3) semifinal victory over Sandrine Testud of France.
The 25-year-old American seeks her fifth victory of the year and 35th of her career. She returned from a three-month absence due to a right knee bruise to win tournaments at Eastbourne and Los Angeles.
Henin has captured three titles this year and reached her first career Grand Slam final at Wimbledon, falling to Venus Williams. The 19-year-old is 0-3 lifetime against Davenport, but has not faced her since the fourth round of the 2000 U.S. Open.
2014: The Year in Music [PHOTOS]