Press, who has scored at least one point in each tournament game, broke through in the 86th minute, bursting through the Pilot defense into the right side of the box and blasting a shot from a sharp angle for her 16th goal of the season.
The game drew a sellout crowd of 2,300 at Cagan Stadium for the matchup of West Coast powers, who both went into the game with one defeat -- 1-0 losses to UCLA.
Portland's frustration continued as the it was eliminated in the quarterfinals of the NCAA Division I Tournament for the third straight year after winning the 2005 title.
The Pilots were missing three players with the U.S. women's under-20 team in Chile -- Michelle Enyeart, Keelin Winters and Elli Reed.
"Let's give Stanford a lot of credit," Portland coach Garrett Smith said. "That had to be one of the best games of soccer played in the country. It was a great game played by both teams and decided by one goal. It was also one of the best defensive performances of the season by our team."
Nov. 28 in Stanford, Calif.
Stanford 1 Portland 0. Goal: Press (McCann) 86.
Stanford -- Maker, Levin, Riley, Falk, Abegg, Jenkins, Noyola, McCann, Press, Taylor, O'Hara. Subs: Stannard.
Portland -- Davis, Nicholson, McCluskie, Tsao, Sweeney, Jackman, Megan Rapinoe, Olivier, Burk, Foxhoven, Schmidt. Subs: Kelly, Kreminski.
Referee: Said Ravanfar.