The Sky Blues conceded four goals in the opening 23 minutes of the second half against an Adelaide side sitting second last on the ladder.
Having won their previous 12 matches against the Reds, Sydney showed none of their normal attacking fluency as Adelaide turned the mounting pressure into a goal frenzy during the opening stages of the second period.
An own goal, a double from Adriana Jones, and late goals to Emily Hodgson and Sofia Huerta ensured Adelaide the surprise win against a disappointed Sydney side.
Meanwhile Perth Glory stole a last-minute 1-0 victory over Western Sydney Wanderers to leapfrog into second, further adding to the Sky Blues' anguish.
Melbourne City will travel to Canberra United for the other semi-final, as they snuck into fourth spot thanks to a 2-0 win over Newcastle Jets on Friday prior to Canberra's 5-1 over Melbourne Victory on Saturday.