Moya, who is tied with Lleyton Hewitt and Andre Agassi for the ATP lead with four titles this year, saved one match point at 6-7 in the tiebreak.
In the only other second-round encounter, fifth seed Jiri Novak of the Czech Republic defeated Argentine qualifier Guillermo Coria, 7-5, 6-2. Novak has not appeared in a championship match this year but has advanced to six semifinals and owns 46 match wins.
Top seed Tommy Haas of Germany rallied past Russian Mikhail Youzhny, 6-2, 2-6, 7-5. Haas was down, 3-5, in the third set, but won four straight games for an emotional victory. His parents, Peter and Brigitte, were sitting courtside to watch him play for the first time since they were involved in a near-fatal motorcycle accident in June.
"The most important thing for me was that my parents were in the stands watching me," Haas said. "The first round is always dangerous, you have to find your rhythm. I'm quite far away from my top form, I'm not moving the way I want to and my (right) shoulder is still hurting a little bit. I have to raise my level in my next match (against Austrian wild card Jurgen Melzer) to win."
Sixth seed Roger Federer of Switzerland also reached the second round with a 7-5, 6-1 triumph over Croatian qualifier Zeljko Krajan, who served for the first set at 5-4. Federer answered by winning four straight games and nine of the last 10.
"I always had difficulties in the first round here in Vienna," Federer said. "He played well, especially in the first set, but I knew I would get chances in almost every game."