Goodson headed home the game-winner off a corner kick in the 105th minute after scoring on a header off Niki Arlitt's cross early in the second half to erase the Wildcats' 1-0 advantage.
Goodson, a product of Southern California's Eagles program, has four goals in four games.
"Goodson is very good at scoring goals," said Longhorn coach Chris Petrucelli. "She got to it in the air, she has a good shot. I thought she did a really nice job possessing the ball as well. Two goals for any player is a great night, but two goals for a freshman is as good as it gets."
KHOSROSHANIN MILESTONE. USC coach Ali Khosroshahin, the 2007 Soccer America Coach of the Year, won his 100th collegiate game on Sunday when the Women of Troy beat visiting Alabama, 7-1. Khosroshahin, who arrived from Cal State Fullerton in 2007, is now 100-44-8 overall.