Mark Sampson's side impressed against the World Cup winners, but they could not respond to Dunn's 72nd-minute goal in the first of a three-match run in the SheBelieves Cup.
It was a fast start from England as Demi Stokes created an early opportunity when she unleashed a left-footed shot, but it was charged down by the USA's defence.
The Lionesses appealed for a penalty in the 35th minute when the ball struck the arm of defender Becky Sauerbrunn, but the referee waved away the claims.
The Manchester City Ladies star had a free shot at goal, but her effort towards the bottom left corner was grabbed by goalkeeper Hope Solo.
The USA delivered a sucker-punch to England when Dunn turned away from Steph Houghton before making her way into the penalty area to score from the left side.
England will play Germany on Sunday and then France next Wednesday.