The triumph provided a timely boost for the cash-strapped side, who are looking for new investors after the directors relinquished their license on Tuesday.
Brisbane, who finished top of the standings in the regular season, looked like having their 27-match unbeaten streak ended when they trailed the Mariners 2-0 with three minutes of extra-time remaining after a scoreless 90 minutes.
The Mariners, led by man-of-the-match Matthew Ryan in goal, defended for long periods as Brisbane dominated possession but they took a surprise two-goal lead thanks to Adam Kwasnik and Oliver Bozanic in the first period of extra time.
However, Brazilian forward Henrique pulled one back for the Roar and then Erik Paartalu headed in a corner just before the final whistle to force a shootout.
"To be honest, I gave up hope and I thought it was one of those days," Paartalu told Fox Sports.
"Full credit to these boys for coming back at the death. We dominated for most of the first part of the game and you have to give credit to Central Coast, they took their chances which we didn't."
Roar goalkeeper Michael Theoklitos then saved Danny McBreen and Pedj Bojic's spotkicks, allowing Henrique to stroke home the winning kick to thrill the majority of the club-record 50,168 crowd at Brisbane's Suncorp Stadium.
