Trailing by double-digits with just over two minutes to go, Monique Conti showcased the Gems' never-say-die attitude as she dived for a loose ball at half-court before feeding Ezi Magbegor for the simple lay-in.
Anneli Maley then drained her first three-pointer of the tournament and Jazmin Shelley followed quickly with an and-one to put together a 7-0 run for Australia.
Russia responded with two free-throws after drawing Magbegor's fifth foul which saw the star centre miss the final 35 seconds.
However, that did not slow down the Gems' momentum as Monique Conti drove in for the lay-up before coming up with a steal and finding Shelley for another triple to tie the game.
Shelley was then called for a tough foul at the other end and Maria Vadeeva sunk both free-throws for Russia but it still gave the Aussies a chance on the final possession with five seconds left.
Chloe Bibby had a great look and a great shot but after the ball looked like dropping on the siren, it somehow rimmed out in the cruelest fashion to see the Gems lose by just two points.
Coming into the Quarter-Final, the match was expected to be a physical arm-wrestle but the Australians found themselves down a soldier pre-game with Maddison Rocci's arm in a sling.
Conti (two points, eight assists, three steals) replaced her in the starting line-up and while Shelley drilled two three-pointers to get things going, the teams combined for just 6-36 shooting for the first quarter as the grinding nature of the contest began.
Nine free-throws for Russia gave them a five-point edge as their tall forwards negated the usual advantage that the Australians had through Magbegor and Zitina Aokuso (three points, five rebounds).
The Gems were up for the fight though and a ten-point run midway through the second term finally saw their offence click with Maley (six points, 13 rebounds) and Bibby (ten points, nine rebounds, two assists) contributing.
Australia's full-court press threw Russia into disarray and they surrendered their lead going into the main break, scoring just three points for the final 7:39 of the half as the Gems clamped down.
Uncharacteristically scoreless through the first half, it only took Magbegor one possession in the third term to get on the board and she connected quickly on back-to-back possessions.
The centre had a block at the other end as well in an enthralling battle with Vadeeva but Russia continued to pound down low to re-take the lead by nine points midway through the third period while forcing Magbegor (nine points, five rebounds, two blocks) into foul trouble.
A couple of offensive fouls saw things begin to unravel for the Gems before Shelley was able to stop the rot with a silky jumper and then Abby Cubillo hit a three-pointer.
The wind was taken out of their sails though with Russia nailing a buzzer-beating three to head into the final change ahead by nine.
Shelley (26 points on 9-18 shooting) provided the perfect start to the fourth quarter with her third three of the contest but Russia answered to push the margin out to double-digits.
The Aussies did not panic though and out of a time-out, coach Dee Butler drew up another play for Shelley to knock down her fourth three-pointer and start Australia's incredible comeback.
Find the box score here and watch a replay of the game vs. Russia below.
The Gems will now play the loser of the China/Canada Semi-Final in the classification game with places 5-8 in the tournament still up for grabs over the next two nights.
Stay tuned to Basketball Australia's social media channels for information on those games as well as a link to the live-stream.
Australia's Schedule for the Under-19 Women's World Championships (all times AEST):
July 29: Classification 5-8 vs. China/Canada
July 30: Classification 5-6 or 7-8