The victory, combined with Denmark's 2-0 win against Norway, clinched first place in Group B and a berth in the championship game on Wednesday at Stadium Algarve in Faro against the winner of Group A. The U.S. will face Norway in its final group match on Monday in Ferreiras.
With the wind at its back in the second half, the USA dominated but couldn't score until Kai's goal.
U.S. captain Christie Rampone, standing on the left edge of the center circle in the USA's attacking half, drove a perfect pass over the top of the Iceland defense to Kai, who brought the ball down on her chest just a step inside the penalty area, let it bounce once and then lifted it over an onrushing Iceland defender. Kai then darted past the defender and ripped a left-footed half-volley into the right corner from 12 yards out to win the game.
March 6 in Ferreiras, Portugal
USA 1 Iceland 0. Goal: Kai 90.
USA -- Barnhart, Mitts, Rampone, Boxx, Chalupny, Rapinoe, Hucles (Buehler, 84), Lloyd, Woznuk (O'Reilly, 46), DiMartino (Tarpley, 46), Rodriguez (Kai, 68).
Iceland -- Gudborg Gunnarsdottir, Gudrun Gunnarsdottir, O.Vidarsdottir, Jonsdottir, Altadottir (Sigurdardottir, 36), Gardarsdottir, Magnusdottir (Honnudottir, 64), Stefansdottir, Larusdottir (Arnardottir, 91+), S.B. Gunnarsdóttir (20-Katrin Ómarsdóttir, 45), M.Vidarsdottir.
Yellow card: USA -- Boxx; Iceland -- Sigurdardottir.
Referee: Bibiana Steinhaus (Germany).