To outfox someone is to defeat them at something using quick thinking or sneaky tricks. Some of the most popular fictional detectives cleverly outfox their foes.
You can attempt to outfox your opponent at poker using tricky strategies and bluffs. A political candidate can also try to outfox a rival, either through smart debate tactics or sneakier, more underhanded means. Outfox has been used in this way since the 1930s, from the old-fashioned verb fox, "to delude or deceive," which stems from the idea (popular in folklore) of foxes being wily or tricky.