Oar found the net with a soaring 30-meter (yard) free kick that went into the top corner.
Australia was outplayed for much of the match and seldom looked threatening against the quicker South Americans.
Juan Govea gave Ecuador the lead in the 24th and his side dominated most of the Group C match until the final minutes.
Ecuador went ahead when Australia keeper Mark Birighitti blocked a shot from Marcos Caicedo at close range but the rebound went to Govea, who drove the ball into the roof of the net.
Marlon De Jesus almost doubled the lead in the 38th, but Birighitti stopped him with a point-blank save. De Jesus also was stopped in the 53rd on a close-range effort.