Oswald, a qualifier into the main draw, defeated Daniel Brands 4-6, 6-2, 6-3 in a first-round match by converting on 3-of-4 break-point chances over the last two sets.
Brands eked the first-set win but Oswald dropped just five points on serve in the second set and seven in the third for his first ATP win of the year.
Seventh-seeded Ernests Gulbis controlled the third set for a 2-6, 7-5, 6-1 decision over Andreas Haider-Maurer, Oswald's countryman. Gulbis won more than 60 percent of the points in the third set.
Two other Austrian players, wild-card entrants like Haider-Maurer, lost first-round matches Monday.
Qualifier Pavol Cervenak beat Ruben Ramirez Hidalgo 4-6, 7-6 (7-1), 6-3 and Simone Bolelli got past Horacio Zeballos 7-5, 7-5. Also Rogerio Dutra Silva was up 4-1 in the first set when Jan Hajek retired.