Begu, who hit seven aces but double-faulted 11 times, will play Hungarian Grand Prix finalist Yvonne Meusburger of Austria or Bosnia's Jasmina Tinjic in the next round.
Also, eighth-seeded Karin Knapp of Italy beat Valeria Solovyeva of Russia 6-3, 6-2, and Arantxa Rus of the Netherlands edged Maria-Teresa Torro-Flor of Spain 7-5, 5-7, 6-4.
Later Monday, top-seeded Mona Barthel played Chiara Scholl of the United States. The German took over the top seeding after defending champion Alize Cornet of France pulled out with a shoulder injury.
Results from the first day of the WTA Bad Gastein Open on Monday (x denotes seeding):
Mona Barthel (GER x1) bt Chichi Scholl (USA) 6-0, 6-0
Arantxa Rus (NED) bt Maria Teresa Torro (ESP x7) 7-5, 5-7, 6-4
Irina Begu (ROM x3) bt Carina Witthoeft (GER) 6-3, 6-3
Karin Knapp (ITA x8) bt Valeria Solovieva (RUS) 6-3, 6-2