Put in to bat at the C.ex Coffs International Stadium, the second-placed Sixers struggled to score quickly on a slow pitch.
They struck six sixes but just nine fours, with Ben Dwarshuis taking 10 off the last two balls of the innings to lift them above 140.
Left-arm spinner Matt Kuhnemann (2-19 off four overs) bowled particularly well, claiming the first two wickets to fall - James Vince and Kurtis Patterson.
A third wicket stand of 47 between opener Josh Philippe (41 off 36 balls) and Moises Henriques (22 off 22) lifted the Sixers to 2-82 in the 13th over.
But the Sixers lost a wicket in each of the next four overs as their innings declined, losing 6-39.
Jack Edwards (22 off 15) and Dwarshuis (13 not out off 6) added some late substance.
Brisbane's bowling variety, execution and slick fielding were instrumental in keeping the score down.
Philippe made his highest score of the season before being caught behind.
Henriques, who became the first man in BBL history to captain in 100 games, was run out at the bowlers end by a direct hit from point by Michael Neser.
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