Spain started out quickly with a win in the first set but appeared to lose momentum after the brief rain delay and dropped the next two sets by identical 6-4 scores.
The final set went through the tiebreaker with neither side able to claim victory until Austria prevailed on the fifth match point.
Spain can still advance to the semifinals with a win in the fifth rubber Sunday between Nicolas Almagro and Austrian Andreas Haider-Maurer.
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