Having won 20 doubles tournaments, the 26th-ranked Czech player improved to 2-6 in career singles finals after winning her maiden title in Quebec City in 2011.
Strycova lifted the trophy at the Austrian indoor event with former seventh-ranked player Barbara Schett looking on. Schett helped the Czech at the start of her professional career in 2003.
"I would like to thank my mentor. When I was 17, she was my mentor and she was still playing, it's Babsi," the 31-year-old Strycova said after the match. "And we are still standing here all together and it's really something special for me."
Strycova broke the top-seeded Rybarikova in the opening game and held on to the advantage to take the first set.
Strycova added three more breaks to take a quick 5-0 lead in the second as Rybarikova looked hampered by a right thigh injury. Strycova dropped serve for the only time in the match but broke back immediately and converted her first match point on Rybarikova's serve to close out the victory.
The 28th-ranked Rybarikova, who lost in the semifinals at Wimbledon this year to eventual champion Garbine Muguruza, was after her fifth career title and first since 2013. She is now 1-4 against Strycova, having beaten her only when they met for the first time 10 years ago.