The Sky Blues twice lead, thanks to goals from Patryk Klimala, but on both occasions Reds striker Archie Goodwin equalised.
Segecic then snatched the winner in the 94th minute to help Sydney climb into sixth spot at United's expense.
Sydney took the lead against the run of play on 19 minutes when a long hopeful ball from Joe Lolley inside his own half caused confusion in the Adelaide defence.
Centre back Bart Vriends and debutant goalkeeper Max Vartuli failed to clear leaving Klimala to take full advantage and roll the ball into an empty net.
Less than two minutes later United should have equalised as they had a one-on-one saved by Harrison Devenish-Meares.
Within a minute of the restart, the Reds drew level through Goodwin.
Panagiotis Kikianis launched a ball out of defence which Jonny Yull ran onto and squared for Goodwin, who tucked it under Devenish-Meares.
On 53 minutes the visitors delivered another sucker punch to make it 2-1. Costa expertly held up possession on the wing before splitting Adelaide's defence, finding Jordan Courtney-Perkins.
The full back drove forward and crossed which Vartuli parried away, but only into the path of Klimala who smashed the ball home from close range.
After a period of sustained pressure, United equalised in the 73rd minute thanks to Goodwin again.
Substitute Yaya Dukuly exhibited some fancy footwork on the edge of the area before lifting a cross to the back post where Goodwin nodded in his second.
Sydney substitute Segecic wasted a glorious opportunity in stoppage time to win the match for the visitors, shooting wide from six metres with just Vartuli to beat.
But the young gun didn't have to wait long to atone, stealing all three points for Sydney in the 94th minute.
His first attempt was well-saved by Vartuli, but the debutant shot stopper couldn't keep out the follow up from Segecic. The low, powerful shot cannoned off the Reds' keeper and into the back of the net.
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