The Jets looked to be cruising towards victory at No.2 Sportsground on Wednesday courtesy of a 27th-minute strike from captain Cassidy Davis.
But the Jets were unable to add a second as Adelaide struck back in the second half with two goals courtesy of substitutes.
Erin Healy got the Reds level on the hour mark before teenager Carina Rossi stabbed home in the 73rd minute.
Adelaide climbed up to fourth with victory with just three points separating Canberra in second and Brisbane in ninth in the battle for a top-six spot.
The Jets sit sixth after Wednesday's loss and would no doubt feel this was a win they should have iced.
The hosts were in a mood from the outset with Sophie Hoban flashing a shot into the side-netting and then hitting the crossbar.
Charlotte Lancaster also had a shot blocked by Holly McNamara and it felt it was a case of when not if Adelaide's resolve would crack.
Lancaster was the provider for the Jets when she whipped in a low cross from the left that found the feet of Davis.
Davis poked home from close range and the Jets should have extended their advantage early into the second half when Kelli Brown was played in on goal.
The New Zealand international couldn't bury her first attempt and then lashed her follow-up effort into the side-netting, her inability to finish proving costly.
Adelaide, who looked to be on the ropes, charged down the other end where Healy was able to nudge home an Emily Hodgson cross in the 60th minute.
Then after a goalmouth scramble following a corner, Rossi was able to hit home to give Adelaide victory with the first goal of her ALW career.
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