Urusei Yatsura

This episode opens with a baseball game and Ataru getting hit with a left field flyball. Ataru is soon escorted home and discovers he's been chosen to fight an invading alien force's champion in a 10-day game of tag. If he loses, the aliens will invade. But if he wins, the aliens will go home. Ataru isn't at all willing to play tag until he sees the alien's champion: the beautiful Lum.