The 23-year-old Serb captured her second title in three weeks to move back into the top 20 for the first time in more than a year, having dropped to a low of 65 in July.
Ivanovic won the first set easily, but the second was much closer, with Kleybanova's double-fault in the tiebreak providing the turning point.
"The second set came down to mental strength and just believing in myself," Ivanovic said. "I managed to stay calm so I was happy to close out the match.
"It's great to win another title, I'm thrilled and it's a big step for me. The last few months have been great and really exciting, and it's a good way to go into next season."
Ivanovic claimed the No. 1 ranking in 2008 after winning her first Grand Slam tournament title at the French Open, but has struggled with her fitness and form since. Her win in Linz last month was her first title since 2008.
The 21-year-old Kleybanova has enjoyed her best ever season, with two titles and now a runner-up finish.
"Ana had a terrific week," Kleybanova said. "I'm so happy to be here, even if I didn't win today. I'll never forget this tournament. It was a great week."