The triumph was Brisbane's eighth from their last 14 visits to Bluetongue Stadium and saw them leapfrog Western Sydney Wanderers to the top of the A-League standings.
Brisbane promoted Dimitri Petratos and James Donachie to the starting line-up with Yeboah dropping to the bench, having failed to find the net in his previous three outings, while Justin Pasfield replaced Liam Reddy in the Mariners' goal and Daniel McBreen returned to the XI, after a loan spell in China.
The Mariners threatened the Brisbane goal twice inside the first 10 minutes with Joshua Rose at the forefront of their attacking play.
A penalty appeal was also waved away by referee Ben Williams, despite home protests, after the ball appeared to strike James Donachie on the arm.
Brisbane worked their way back into the game as the half went on though, with Henrique Silva wasting a pair of good chances and Thomas Broich just failing to get on the end of Dimitri Petratos's chipped pass.
Mitchell Duke found himself clear on the Brisbane goal in the final minute of the first half, but failed to test Michael Theo.
Reddy, making his first A-League appearance since being sacked by Sydney FC in March 2012, was in inspired form at the other end as the visitors turned the screw after the break.
Ivan Franjic forced the 32-year-old into an acrobatic save on 67 minutes and he was again sharp soon after to keep Petratos out from close range.
Rose almost snatched the points for the Mariners in the 87th minute, but saw his crashing drive come back off the post.
And 19-year-old Yeboah, who entered the game a minute later, struck less than 60 seconds after being introduced, bursting into the penalty area and firing his first A-League goal past the undeserving Reddy.
