Bryce Hegarty provided 16 points as the Reds moved up to fourth in the Australian Conference courtesy of a convincing win at Suncorp Stadium.
Higginbotham went over from close range in the first half for the Reds, who took a 10-0 lead into half-time.
Henry Speight, on his 31st birthday, scored in the corner shortly after the break to bring the Brumbies back into the game.
FULL-TIME | REDS v BRUMBIES
A comfortable bonus-point victory for the Reds, who secure their second Super Rugby win of the year.
— Super Rugby (@SuperRugby) March 24, 2019
However, converted tries from Feauai-Sautia and McDermott helped the Reds pull clear before they added to the scoreboard late.
It gave the Reds back-to-back wins after they started the season with three straight losses, leaving them just four points behind conference leaders the Waratahs.
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