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Hewitt beat John Isner 6-1, 7-5 while Stosur defeated Melanie Oudin 6-2, 6-4 to give Australia a winning 2-0 lead.
The US salavged some pride in winning the mixed doubles when Oudin and Isner beat Stosur and Hewitt 2-6, 6-1, 7-6 (10/5 match tiebreak).
The US has won the Hopman Cup five times and been runner-up on four occasions.
The win evened Australia's record at 1-1 while the US fell to 0-2.
In another Group A match on Tuesday, Spain take on Romania, each of those teams with 1-0 records.
The team with the best record in each of two groups advances to Saturday's final.
Hewitt won the first three games of his match with Isner in just eight minutes, and faced a break point while serving for the set before hitting two aces to win. He broke Isner's service in the 11th game of the second set, then held service to clinch the match.
Stosur lost in three sets in Australia's opening match to Romania's Sorana Cirstea.
"It's a lot better walking off the court a winner than a loser," Stosur said. "I thought I played pretty well today."
Stosur won the first set in 26 minutes but faced a tougher test in the second, saving three break points before securing a break of her own to open a 4-2 lead. She converted three of seven break-point opportunities and had 14 aces.
Russia and Britain, each 1-0, play their Group B matches on Wednesday. The British, led by Andy Murray, take on Germany, while Russia play Kazakhstan.
