Australia had been languishing in fifth after a solitary victory over Kazakhstan, but the win saw them shoulder Greece out of the fourth and final qualification spot.
Australia, playing in green and gold caps against the white of Greece, raced away midway through the game and Greek captain Georgios Afroudakis had no complaints about the result.
"They deserve to go to the last eight," Afroudakis, appearing at his fifth Olympics, said. "We go back home unhappy, but that's sport."
Croatia had already wrapped up the group before their 12-4 win over Kazakhstan on Monday, but centre forward Niksa Dobud said the knockout rounds were all that mattered.
"It don't mean nothing before the quarter-finals. If we lose there, we go home," Dobud said.
Australia and Croatia's next opponents will be decided by the outcome of Group B games to be played later on Monday.
Croatia went through unbeaten from their pool, though it is regarded as the easier of the two groups. On current standings, Croatia could face defending champions Hungary, who are gunning for their fourth consecutive gold.
"Hungary didn't play any game like they can. I'm scared that Hungary can play like they did in the Olympics before," Dobud said. "I'm scared if they play like that in the quarter-finals."