A 24th minute goal from Juan Govea looked likely to give Ecuador a deserved win against a misfiring Young Socceroos outfit in the Group C fixture in Manizares.
However, winger Oar's perfectly executed 30 metre left foot curler in the 89th minute secured a precious point for Australia.
Ecuador manufactured the majority of clear cut chances after their goal as their pace and passing ability caused plenty of problems for the Young Socceroos.
Australian goalkeeper Mark Birighitti kept his team in the game with several fine saves.
Spain thrashed Costa Rica 4-1 in the other Group C fixture.
The Young Socceroos play Costa Rica on Thursday (AEST) and Spain on Sunday (AEST).
Australia's passing inside the Ecuadorian half lacked penetration and their main attacking players rarely threatened.
Midfield playmaker Mustafa Amini struggled to make an impact, while striker Kerem Bulut and wide men Kofi Danning and Oar were also well contained.
Australia's brightest attacking moments came mainly in the first 14 minutes.
They missed a glorious opportunity to hit the front inside the first 30 seconds when Danning blazed over from close range.
Amini shot wide from the edge of the area and Marc Warren had a header pushed away by Colombian goalkeeper John Jaramillo.
The Ecuadorian goal came after Marcos Caicedo rounded Warren, when his cross from the byline was pushed out by Birighitti and Govea blasted home from close range.
Ecuador then took control and bossed the midfield, manufacturing all the other decent first half opportunities as Birighitti pulled off three fine saves, two of them from close range.
Ecuador also threatened early in the second half, with Govea heading over from a corner and Birighitti saving well from Marlon De Jesus.
Australian coach Jan Versleijen made two early second half changes.
He replaced Amini with his youngest player, 17-year-old midfielder Terry Antonis and striker Bernie Ibini-Isei came on for skipper Ben Kantarovski, who was playing his first competitive match in several months.
Antonis added some spark and Australia looked a little more dangerous in the final third of the game.
Oar dragged a shot wide in the 66th minute and Bulut headed over from a corner 11 minutes later, before Qar produced his equalising shot.
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