Midfielder Nick Fitzgerald scored with the follow up from his own missed penalty to restore parity in the 79th minute and then full-back Josh Rose fired an 83nd minute winner as the match turned on its head.
Awer Mabil had given the second-placed Reds the edge with a first half strike, and they appeared to be coasting before the Mariners' late revival in front of a disappointing crowd of just 4,508.
The Mariners, who were crushed 5-1 by Sydney FC in their last home appearance, showed far fortidude on this occasion.
The win was a much-needed boost for Central Coast, which was seven points shy of the top six before the round-16 game.
Coach Phil Moss said the Mariners, like Newcastle in the 2-1 loss to Brisbane on Friday night, were desperate to bounce back from a forgettable performance.
"I think today was about building some pride back in the shirt," Moss said. "I sound like I'm talking like Phil Stubbins from last night, but it was the same for us.
"We weren't happy to cop five goals at home and lose to Sydney, so we worked hard on the mentality of the players between then and now.
"Were we good today? Was it pretty? No. But we found a way to win the game and that shows the mental resolve of the players."
For the Reds, it was an opportunity missed in their hunt for the minor premiership.
Disappointed with the result but pleased with the way his side played, Adelaide coach Josep Gombau believed his team suffered from complacency after going ahead.
"After we score the goal, we had control and it's 1-0 but we can't afford to have that feeling that we will win," Gombau said.
"Because any single action from the other team, they can score and you can lose the game, and today that happened.
"I think it will be a lesson for us, but this is football and we have to learn from our mistakes."
Young gun Mabil, recently back from a trial with Ajax, was in the right place to turn and thrash the ball home via a deflection off Jacob Poscoliero from Sergio Cirio's asute cutback to give Adelaide a 28th minute lead.
Lacking in confidence and belief, Moss's side found the going tough and a scuffed first-half shot from Fitzgerald, when well placed, didn't help their cause.
The Reds had a strong shout for a penalty waved away in the 38th minute when Cirio appeared to be tugged down by Storm Roux.
Osama Malik should have added a second for the Reds in the 50th minute but he badly miscued his header from a corner.
Central Coast hit back when Michael Marrone handled a scuffed shot from Fitzgerald, and though Eugene Galekovic parried his penalty, he buried the loose ball.
Then Mitchell Duke picked out the run of Rose with a perfect pass, and he buried the clincher with some aplomb.
The win was a much-needed boost for the Mariners, who were seven points shy of the top six before the round-16 game.
It was an opportunity missed for the Reds in their hunt for the minor premiership.
The visitor had a stranglehold on the game with their speed, touch and passing in midfield but could not land the knockout blow.
Former Real Madrid winger Miguel Palanca made his debut for Adelaide, coming on the 62nd minute for Bruce Djite.
New Mariners recruit Fabio Ferreira watched on due to a gentleman's agreement between the clubs that he would not play against his former team.
