The day began in winning fashion for the No.3-seeded Knapp, who battled for more than two and a half hours to make it past No.1 seed Sara Errani a rain-postponed semifinal match, 7-6(4), 4-6, 7-5.
And it looked like her momentum from that victory was carrying over into the final - Knapp jumped out to a 6-3, 4-2 lead with three points for 6-3, 5-2, and she even served for the match at 6-4, 5-4.
But the No.2-seeded Stosur wouldn't go down without a fight, rallying to win the second set in a tie-break and then cruising through the third set to win in two hours and 28 minutes, 3-6, 7-6(3), 6-2.
"It was a very hard match today," Stosur said. "I was getting completely outplayed in that first set, and even though she was up in the second set too, I started to feel like I was doing a little better. Obviously she served for the match but I hung in there, got that set then played better and better from there.
"It's not ideal to be playing a semifinal and final in one day, a two-and-a-half-hour match in the morning then another two and a half hours in the afternoon, but unfortunately that's just what happens with the weather sometimes. And she did serve for the match, so she wasn't doing too badly either."
"It wasn't easy to play five hours today but I was really fighting. I just missed some chances, and she used hers," Knapp said. "It was a great week, though. I'm looking forward to the next tournaments."
It was Stosur's eighth WTA title after winning Osaka in 2009, Charleston in 2010, the US Open in 2011, Carlsbad and Osaka in 2013, Osaka in 2014 and now Strasbourg and Bad Gastein in 2015.
Will Stosur come back to defend her title next year?
"I'd love to come back," she commented. "I've said all week, it's a beautiful place and I've really enjoyed being here. I love being in the mountains - it's something quite different for us from Australia.
"And it's my last week in Europe for a long time - it's been a good place to finish the trip."
The doubles title went to Danka Kovinic and Stephanie Vogt, who upset No.1 seeds Lara Arruabarrena and Lucie Hradecka in the final, 4-6, 6-4, 10-3. Vogt now has two WTA doubles titles, having won Luxembourg with Yanina Wickmayer in 2013, and Kovinic took home her first WTA title of any kind.