Taberner led the forward line with five goals in the 23.9 (147) to 9.10 (64) result, which looked unlikely after Brisbane opened the game with three majors.
Many considered it a breakout game for the 22-year-old who has shown real signs of improvement this year, even in the absence of a host of stars.
After being jumped early, the Dockers clawed their way back into the Gabba clash.
The visitors booted nine goals to just one in the second term as the hosts capitulated badly.
The Dockers consolidated their dominance in the second half to record their second win of the season.
Most impressive were the Fremantle youngsters.
Taberner’s five goals came along side Connor Blakely’s team-high 29 disposals, Lachie Weller’s 22 disposals and four goals, and Darcy Tucker’s 19 disposals, seven inside 50s, and two goals.
Lachie Neale, Fremantle’s best player this season, was held to 18 disposals. Michael Walters had 19.
Hayden Ballantyne had his best game for some time with 23 disposals and four goals.
Stephen Hill kicked superbly out of the back pocket, and Danyle Pearce had a team-high eight inside 50s.
Fremantle’s next match is against Port Adelaide on Saturday at Subiaco Oval.