The 19-year-old striker had been on the field for just a few minutes when he burst into the area to blast an unstoppable drive past goalkeeper Liam Reddy in the 89th minute to guarantee a deserved victory for the visitor.
The win sent Brisbane back to the top of the A-League - a point clear of Western Sydney Wanderers.
Reddy had made a triumphant return to the A-League with a string of fine saves but could do nothing to deny Yeboah.
Sacked by Sydney FC 19 months ago following a drinking incident on board a flight to New Zealand, Reddy was walking on air after keeping Brisbane at bay before Yeboah's telling intervention.
Roar had the better of the first half, pressing high to make it hard for Central Coast to play out with any genuine purpose from the back.
But it was the Mariners who had a decent shout for a penalty denied by refereee Ben Williams after Roar defender James Donachie appeared to handle in the 14th minute.
The decision left Mariners coach Graham Arnold fuming after a linesman's flag initially indicated it should have been a spot kick.
Chances were scarce, but Brazilian Henrique forced Liam Reddy - handed his first A-League start this season as Arnold axed first-choice keeper Justin Pasfield - into a smart save in the 37th minute.
Then Socceroos midfielder Matt McKay angled his shot just wide to the relief of the home side when found in space inside the box by Jack Hingert's cross late in the half.
On the stroke of half-time fellow Socceroo Mitchell Duke wasted an even better chance when he burst down the middle only to fire straight at keeper Michael Theo.
The game marked the return of last season's A-League Golden Boot Daniel McBreen from his successful loan spell in China - but the veteran striker was tighly contained by Brisbane.
Reddy came to Central Coast's rescue again on the hour - tipping away a crisp shot from new Socceroos call-up Ivan Franjic.
He was called into action again in the 73rd minute to make a fine reaction save from Dimi Petratos after a Corey Brown cutback.
Two minutes later Trent Sainsbury was the saviour, clearing off the line after Henrique had wriggled past Zach Anderson and squeezed his shot past Reddy.
The Mariners came closest in the 88th minute with defender Josh Rose rattling the post with a low shot - but it was Yeboah who stole the show a minute later after coming on in place of Henrique.