During the Games, Katniss and Rue had formed an alliance. When Katniss went to retrieve a bow and arrow, she returned to find Rue trapped in a net by Clove, one of the Careers. Clove was preparing to kill Rue, but Katniss shot an arrow at Clove, distracting her. Rue was able to escape, but Katniss was left to face Clove and the other Careers alone.
While Rue didn't directly save Katniss from physical harm, she did allow Katniss to escape from the immediate threat of Clove. This act of bravery and sacrifice solidified the bond between Katniss and Rue, and played a significant role in the development of Katniss's character.