The young striker filled the void left by the injured Besart Berisha by rifling home a late goal to see Mike Mulvey's side end the weekend at the summit of the A-League ladder.
Yeboah's stunning late strike saw Brisbane leapfrog the Western Sydney Wanderers back to the top of the A-League ladder after a match in which they dominated possession.
Brisbane elevated Dimitri Petratos and James Donachie to the starting line-up with Yeboah dropping back to the bench having started last week.
Graham Arnold sprung a minor surprise in replacing Justin Pasfield with Liam Reddy between the posts.
The home side also saw Daniel McBreen return from his loan spell in China to start alongside Marcel Seip as the outfield duo replaced Kiwi internationals Michael McGlinchey and Storm Roux.
Twice inside the first 10 minutes the Mariners threatened the Brisbane goal with Joshua Rose creating two chances as the home side showed some enterprise early.
Three minutes later the Mariners were on the attack again and had a penalty appeal waved away by referee Ben Williams after the ball appeared to strike Donachie from close range on the arm.
Following that the teams traded hopeful chances with Brisbane's Ivan Franjic and the industrious Rose for the Mariners at the forefront.
The Roar then had three chances in the space of four minutes.
Two fell to Henrique who failed to control a lobbed ball and then ripped an effort from outside the penalty area which Reddy saved to his left.
Influential German Thomas Broich also failed to get on the end of a Petratos chip angled towards goal as Brisbane dominated first-half possession.
Each side could have scored in the last minute of the half with Matt McKay for Brisbane and then Mitchell Duke for the men in yellow and navy failing to convert their opportunities.
Duke especially should have done better as the ball broke to him unmarked with only Roar 'keeper Michael Theo to beat.
As drizzle started to fall in the second stanza Brisbane continued to dominate possession with chances to Franjic and Jack Hingert, as Socceroo Franjic in particular caused trouble for Reddy.
Reddy, formerly of Sydney FC, had to think quickly in the 68th minute as Brisbane were sharp to take a free kick which he parried away low down to his left.
Petratos forced Reddy into a point-blank save six minutes later when he shot towards goal from eight metres out after Corey Brown delivered a neat ball from inside the box.
For all of Brisbane's dominance, the Mariners nearly snatched it late as fullback Rose struck the left-hand post before Yeboah, who came on for Henrique, took a neat touch before firing into the roof of the net after he had only been on the field for two minutes.
Central Coast Mariners 0
Brisbane Roar 1 (Yeboah 89m)
Crowd: 8,303 @ Bluetongue Stadium