A five-goal burst in the second quarter gave the Tigers a 20-point halftime lead, which they converted into a 20.12 (132) to 12.12 (84) victory in front of a crowd of 22,311 at the Gabba.
Brisbane needed a strong start to the second half but Richmond made the third quarter their own with six goals, four of them going unanswered.
The Lions, who have now lost 11 consecutive quarters of football, fought back in the final quarter and kicked five unanswered goals to close the margin to only 14.
But two goals to Robin Nahas and Shane Tuck in the space of 30 seconds fired the Tigers into a six-goal scoring spree and saw them blow out their lead once more.
Richmond's record against Brisbane is impressive, having now lost only one match from their past ten meetings.
The Tigers moved four points clear of the Lions on the ladder but they remain in 12th position.
Robin Nahas and Luke McGuane top-scored for the visitors with three goals apiece.
Ruckman Ivan Maric (41 hit-outs, 16 disposals, one goal) and centre Brett Deledio (33 disposals, one goal) also put in robust performances.
Lions captain Jonathan Brown led his side with nine marks, four goals and 14 disposals, and was supported strongly by Daniel Rich (22 disposals) and Dayne Zorko (19 disposals, two goals).