The Wimbledon runner-up, sporting a blue and pink dress and Polish-flag nails, did not get off to a good start, being broken in the opening game of the match to go 2-0 down.
The 23-year-old looked to have regained her stride in the second set tie break, storming to a 5-0 lead. Despite the valiant German Goerges clawing it back to 6-5, a shot into the net handed Radwanska the set and they entered a decider.
The match, for two hours the only tennis at Wimbledon after a downpour of rain delayed the start of play on outdoor courts, saw both players winning a break in the third set to keep the score board level.
An increasingly frustrated Radwanska, who carried the Polish flag in Friday's opening ceremony, threw away the chance to break again at 4-4, instead handing her opponent the opportunity in the following game with a shot wide.
Goerges was not so careless, snatching her victory with a forehand down the line.
Radwanska's hopes of a medal now lie in the doubles. She and sister Urszula will play their opening match against Slovakia's Daniela Hantuchova and Dominika Cibulkova later on Sunday.