In her first final of the season, the second-seeded Bacsinszky will face either Alize Cornet or Julia Goerges. Their semifinal was canceled due to rain and rescheduled for Sunday 0800 GMT. The final will be played later Sunday.
The 52nd-ranked Swiss player could win her second career title after Luxembourg in 2009.
Bacsinszky lost all four service games in the opening set when she struggled to find the right length in her ground strokes.
Bacsinszky, who was beaten by Meusburger at the Australian Open in January, took control afterward. She won the second set after saving two break points at 5-4.
In the decider, Bacsinszky was 4-3 up and 15-40 down on her serve when she suddenly left the court, claiming that rain had made the clay surface too slippery.
However, the umpire persuaded her to play on. Bacsinszky came back after a couple of minutes, won that game and broke Meusburger in the next with a return winner on her first match point.
The Gastein Ladies is the last clay-court tournament of the WTA Tour season.