The win means the Australians will have the opportunity to play France in a battle for fifth place on Sunday.
Liz Cambage continued her break out tournament, finishing the game with 19 points and eight rebounds, while Lauren Jackson (17 points, nine boards) and Penny Taylor (19 points, eight boards) improved dramatically from their disappointing efforts against the Czechs.
Svetlana Abrosimova, a teammate of Jackson's at WNBA team Seattle top scored for he game, finishing with 20 points.
Australia and Russia met in the gold medal game at the 2006 World Championship, which the Opals ultimately won, so for the two to meet in the classification rounds is a huge surprise for many punters, who anticipated these two nations were bound for the semi finals.
Neither team had missed out on a medal at Olympic or world championship play since the 2000 Olympics, where Russia finished sixth, but they both will in the Czech Republic.
The Australians have dominated head-to-head battles at major tournaments for more than a decade, beating them in the semi-finals at the 2008 Olympic Games and in the gold medal match at the 2006 world titles.
And they still haven't lost to Russia in a major tournament since a semi-final defeat back at the 1998 world championship.
After such a pulsating game in front of a packed crowd in Friday night's prime-time clash with the host nation, there was a terribly hollow atmosphere in a match that tipped off at 1.15pm local time (2115 AEST) between two fallen giants.
The shock from Friday's result was still evident on the Australians' faces on the team bus on the way to the game and during the warm-up as the reality of the situation hit home.
The game started virtually in slow motion, with the Australians opening up a 14-6 lead before Russia closed with an 8-0 run as a low-quality quarter fittingly ended tied at 14-14.
A 13-4 streak by the Russians gave them a 34-25 buffer late in the half, but the Australians reeled off seven unanswered points to end the half down 34-32.
The Opals then won the third quarter 18-14 to give themselves a two-point lead heading into the final term, before hanging on for a much needed victory.
After a poor long-range shooting performance in their last game, the Opals spent a lot more time inside the arc, only putting up eight three-point attempts. All their offence came from much closer range and it was effective.
The Opals were also much stronger on the boards, dominating the Russians 44-28 and a much more effectively executed game plan.
The Opals now face France this Sunday to decide which team will take home a fifth placing.
By James Dampney, AAP
Australia 78 (Liz Cambage 19 points, 8 rebounds; Lauren Jackson 17 points, 9 rebounds)
defeated
Russia 73 (Svetlana Ambrosimova 20 points, Maria Stepanova 16 points)
Aus Rus
1st Q 14 - 14
2nd Q 18 - 20
3rd Q 18 - 14
4th Q 28 - 25
