The teams split Sunday's reverse singles after the United States had already secured its quarterfinal spot by winning Saturday's doubles.
American team captain Patrick McEnroe rested Andy Roddick and James Blake and let doubles pair Bob and Mike Bryan play the meaningless reverse singles.
Mike Bryan withdrew with an injured left hamstring in the second set against Stefan Koubek to give Austria its only point. Bob Bryan posted a 6-0, 3-6, 7-6 (3) victory over Werner Eschauer, who substituted for Jurgen Melzer.
The Americans will host France, which beat Romania in the first round, on April 11-13 for a place in the semifinals.
Austria lost its opening tie in the World Group for a fifth straight year and will enter the playoff round in September.
Koubek led 7-5, 1-0 when Mike Bryan retired. The American doubles specialist was playing his first Davis Cup singles match.
Eschauer had 12 unforced errors while losing the first set in just over 20 minutes. The 58th-ranked Austrian converted his first break point at 2-2 in the second and broke Bob Bryan again at 5-3 to win the set.
Both players held serve in the final set until 5-5, when Bryan broke at love. He then failed to convert two match points on his serve before Eschauer broke back, but the American took a 6-1 lead in the tiebreaker and converted his fifth match point.
[Associated Press; By ERIC WILLEMSEN]
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