The match marked the first game and first victory for new U.S. head coach Tom Sermanni, a Scotland native.
Press volleyed the U.S. into an early lead in the 13th minute after the Scottish defense failed to clear a log free kick into its penalty area by Ali Krieger.
The 24-year-old netted her second 19 minutes later, slipping past a defender on a well-timed run and heading a Tobin Heath cross in the lower left corner of the net.
Forward Alex Morgan, recipient of the 2012 U.S. Soccer Female Athlete of the Year award, had to depart the game in the first half after she injured her ankle on a Joanne Love foul that drew a yellow card in the 39th minute.
Veteran Shannon Boxx gave the USA a 3-0 advantage in the 52nd minute, receiving a pass from Press with her left foot, bringing the ball to her right and finding the upper left corner from 25-yards out.
Kim Little pulled one back for Scotland in the 55th, drilling an effort past second-half goalkeeper Nicole Barnhart to make the score 3-1.
Sydney Leroux, who replaced Morgan, capped off the scoring in the 89th minute by lifting the ball past the onrushing Scottish goalkeeper Gemma Fay and into the net from 10 yards out. All of Leroux's 15 career goals have come as a substitute.
The U.S. and Scotland face each other again on Wednesday at LP Field in Nashville, Tennessee.