Playing in her first WTA event, Moser broke Barthel twice to take the opening set and the Austrian wildcard was a break up in the second when the 31st-ranked Barthel withdrew.
In the quarter-finals, Moser will play either Andrea Hlavackova of Czech Republic or Viktorija Golubic of Switzerland.
Also, No. 8 Karin Knapp of Italy advanced to the quarters after beating Alexandra Cadantu of Romania 7-6 (5), 4-6, 6-1.
In first-round play, Yvonne Meusburger routed Jasmina Tinjic of Bosnia 6-0, 6-0.
The Austrian conceded just three points on her serve, including a double fault.
Results from the third day of the WTA Bad Gastein Open on Monday (x denotes seeding):
Lisa-Maria Moser (AUT) bt Mona Barthel (GER x1) 6-2, 4-3 - retired
Andrea Hlavackova (CZE) bt Viktorija Golubic (SUI) 5-7, 6-1, 6-0
Karin Knapp (ITA x8) bt Alexandra Cadantu (ROM) 7-6 (7/5), 4-6, 6-1
Yvonne Meusburger (AUT) bt Jasmina Tinjic (BIH) 6-0, 6-0