"A win is a win," said the relieved top seed and world number five who was playing his first match since Spain's Davis Cup final victory over the United States in December.
Moya took the first set easily against his 257th-ranked opponent but was 3-0 down and struggling to handle the Austrian's fierce returns in the second set.
Eventually Moya rallied to claim the tiebreak 7-4.
Second seed Paradorn Srichaphan was given an even sterner test, the Thai staving off two match points before overcoming Belgian Christophe Rochus 4-6, 7-6, 6-1.
"I'm very happy I hung in there," he said after the near two-hour match.
The 2003 winner, ranked 27 in the world, struggled to find his rhythm and faced an early exit when the 112th ranked Rochus held match point serving at 5-3 in the second set.
Although Paradorn fought back, the Belgian had another opportunity with the Thai serving at 5-6, 30-40, but he hit a forehand wastefully long.
Fifth seed Kenneth Carlsen of Denmark wore down Israel's Noam Okun 7-6, 6-4 while fourth seed Jonas Bjorkman of Sweden eased past teenage wildcard Karan Rastogi of India 6-4, 6-0.
Swede Bjorkman, however, said his priority at the tournament was to get all players to contribute money to help victims of the tsunami disaster in the region.
"It doesn't matter what kind of job you've got, everyone has got the disaster on their minds," he said. "Everyone here has got to do the best they can."
More than 200 people lost their lives on the coast of Madras, the capital city of the southern Tamil Nadu state where thousands perished in the December 26 catastrophe.
"Hopefully we can give something and make everyone stronger after what happened," Bjorkman said.
"It was a good decision to come and support the tournament, to shine a little light in the dark."