Their lacklustre performance came just hours after reports surfaced that coach Mark Rudan will be leaving at the end of the season.
Inspirational in his rookie campaign in charge, Rudan is yet to confirm his departure but he has immediate issues to contend with as the Phoenix wheels begin to wobble.
Their first-half display was as meek as in last week’s 3-1 loss in Adelaide.
They allowed ample room for young Brisbane forwards Dylan Wenzel-Halls and Nick D’agostino to run at the back three and the 2-0 halftime score could easily have been greater.
Beautheac’s 37th-minute opener was a solo effort, jinking past lunging defenders before beating goalkeeper Filip Kurto from a tight angle.
Five minutes later he tapped in a low cross from Wenzel-Halls which was poorly handled by the static Phoenix defence.
It lifted Beautheac’s career tally in Brisbane to eight goals from 44 games, giving some hints of the quality promised when signed last season.
The 31-year-old blotted his copybook when sent off following a second yellow card deep in injury time.
Former Newcastle United defender Steven Taylor pulled a goal back with a rifling header from a corner in the 53rd minute for the Phoenix but it failed to inspire his teammates until two blatant late chances were created.
Reserve forward Cillian Sheridan’s close-range strike found the inside of the post while David Williams had the goal at his mercy after rounding Jamie Young but somehow shot wide.
Brisbane tired noticeably but their injury-ravaged team warranted a fourth win of the season.
Midfielder Zach Duncan made his maiden start while 17-year-old schoolboy Izaack Powell was employed at left back.