Sydney took the lead through teen sensation Tiago Quintal in the 14th minute, before Ryan Kitto equalised for Adelaide three minutes later.
In the 80th minute, Quintal went down grabbing his hamstring after slipping on the Allianz Stadium turf - which had hosted Super Rugby the previous night.
But Adelaide snatched all three points when Devenish-Meares, who had been excellent all night, fumbled a relatively tame shot from Luka Jovanovic over the line in the 87th minute.
"He was having a blinder until he took that unlucky deflection with my goal," Jovanovic told Network Ten.
"And it's unlucky for him. He should keep his head high, because he's a very good keeper."
It sent Adelaide, who are without captain Craig Goodwin (groin) for up to 12 weeks, third on 26 points, ahead of Sydney (25) and behind Newcastle (33) and Auckland FC (28).
"Three points means a lot, especially with how tight the table is," Jovanovic said.
The Sky Blues snatched the advantage after Adelaide goalkeeper Joshua Smits failed to fully clear the ball.
Paul Okon-Engstler pounced on the loose ball outside the box and drove forward.
While the Socceroos midfielder was tackled by Ryan White, the ball spilled out to Quintal, who ripped a fierce left-footed near-post strike between Smits' legs.
Adelaide responded after a nice build-up ended with Jay Barnett cutting back for Kitto to volley home.
Sydney's Pedro Quispe and Joe Lolley spurned chances, and Marcel Tisserand thumped a header off the crossbar in the 43rd minute.
Rhyan Grant turned a gilt-edged chance wide early in the second half, before new signing Apostolos Stamatelopoulos headed over the bar in the 62nd minute.
New signing Ahmet Arslan forced a big save from Smits shortly after.
"We never had to lose this game. We don't want this result," Arslan told Network Ten.
"I had two or three chances, some good balls and actions, but I have to score, and when I score, maybe (we) win this game."
Devenish-Meares came up big to deny Ethan Alagich in the 73rd minute, then Yaya Dukuly in the 76th.
But his late error, after Jovanovic burst down the left and shot straight at him, proved crucial - and devastating.
Sydney next host Auckland on Tuesday, and Adelaide play Perth at home on Friday.
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