Russia put up a solid defence for the first seven minutes, before centre Berrick Barnes went over for the Wallabies' first try, which fullback James O'Connor could not convert.
Winger Drew Mitchell got Australia's second from an up-and-under play, and this time O'Connor managed the kick.
The Wallabies' third came minutes later after a cross-field kick and a series of well-timed offloads gave number eight Ben McCalman the opportunity to go over, and openside flanker David Pocock secured a bonus point shortly after when he slid off three Russian tacklers to crash through the posts.
Pocock picked up his team's fifth, which seemed to spur Russia into a sustained period of attack that resulted in an unconverted try from winger Vladimir Ostroushko.
Russia's elation was short-lived, however, as Australia responded almost immediately with tries from hooker Stephen Moore and centre Adam Ashley-Cooper, while O'Connor achieved a conversion rate of six from seven to make the scores 47-5 going into the break.
Replacement Salesi Ma'afu earned Australia's eighth, followed by Mitchell's second and a successful drop goal for Russia.
Mitchell was away for his hat-trick, but pulled up with what looked like a hamstring strain and limped off the field to add to Australia's injury woes.
Russia winger Denis Simplikevich went over from a breakaway run to put more points on the board for the Bears, followed by a try from replacement Konstantin Rachkov.
The Bears looked desperately for a fourth try and a bonus point, but Australia stood firm and Barnes got the final try of the game to make the scores 68-22 at the whistle.
Australia will wait for the result of Ireland's clash with Italy later today (Saturday) to see who they will face in the quarter finals, while Russia will return home from their first Rugby World Cup with the achievement of scoring three tries against the Wallabies.