The Tigers' red-hot pressure and slick ball-use overwhelmed their opponents early as a five-goal opening term laid the platform for a 10.8 (68) to 3.4 (22) victory on Saturday at Coffs Harbour.
Brennan's game-high tally of three majors was complemented by two each from Maddy Shevlin, Sarah Hosking and Mackenzie Ford.
Ellie McKenzie was best afield with a career-high 23 disposals, with Grace Egan (19 touches) and lead ruck Poppy Kelly (38 hit-outs) also outstanding.
The result, in the first AFLW meeting between the sides, gave Richmond a 2-1 record ahead of another winnable game against Carlton on Thursday night.
Sydney (1-2), who lost co-captain Chloe Molloy to a season-ending knee injury last week, have lost consecutive games and face a derby clash with GWS in round four.
Montana Ham (two goals) was a shining light in attack for the Swans and Laura Gardiner worked tirelessly for a game-high 29 touches.
The Tigers' engine room and forwards were on fire early as they opened up a 30-point lead by quarter-time.
The 5.1 to 0.1 scoreline marked Richmond's second-best first quarter in their AFLW history.
Brennan had three goals from her first three kicks opposed to Alice Mitchell and snared three of the Tigers' seven marks inside-50 in the first-quarter onslaught.
Sydney finally mustered a response when Ham kept her feet in a contest and slotted her first major early in the second quarter.
The midfield battle evened up before half-time, but Richmond maintained their buffer through efficiency in attack and were not seriously threatened after the main break.
The Tigers' total of 68 points was their second-highest in AFLW history.
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