The 65th-ranked Goerges, playing in her first final, broke Bacsinszky three times and won the opening set when the second-seeded Swiss player double-faulted on set point.
Bacsinszky led 4-2 in the second set but then was broken twice as the 21-year-old Goerges wrapped up the victory.
"I've played really well all week," said Goerges, who laid down on the court in celebration.
"It was my first final and I just wanted to enjoy it as much as possible. I didn't put pressure on myself," said Goerges, who won five events on the lower-ranked ITF circuit.
Andrea Petkovic of Germany also clinched her first title in Bad Gastein last year.
It was the first final of the season for the 52nd-ranked Bacsinszky, who is now 1-1 in finals after winning in Luxembourg in 2009.
Goerges dictated the pace in the opening set with strong shots from the baseline which forced Bacsinszky into errors.
Bacsinszky succesfully slowed down her opponent with high top-spin shots in the second set, but Goerges again found her rhythm after she lost serve when trailing 3-2.
The German netted a forehand on her first two match points but converted the third with a drop shot.
Earlier Sunday, Goerges beat France's Alize Cornet by the same score in a semifinal that was rescheduled from the previous day because of rain.
Goerges dominated the first set with powerful ground strokes and converted all three break points against Cornet. Both players struggled to hold serve in the second set before Goerges won on her first match point.
The $220,000 Gastein Ladies was the last clay-court tournament of the season.