The Serb's 6-4, 7-6 defeat at the $2 million Tokyo event follows her first-round exit from the US Open earlier this month, underlining a mystifying loss of form.
"I know how Ana is feeling and I feel it with her," a sympathetic Safarova said.
"She's struggling with her serve and when that goes, all your game goes."
Safarova's win was arguably the highlight of a low-key opening day at the lucrative Pan Pacific Open, featuring nine of the world's top 10 women.
World number one Dinara Safina, last year's Tokyo winner, second seed Venus Williams and French Open champion Svetlana Kuznetsova begin their campaigns on Monday.
Japan's Kimiko Date Krumm will get little time to savour winning her first WTA Tour title in 13 years in Seoul on Sunday as the wildcard is also in action on Monday, her 39th birthday.
Safarova had lost two of her previous three meetings with Ivanovic, one of them at last year's French Open when the Serb went on to win the title before reaching number one.
But there was little grand slam pedigree in Sunday's encounter as the 21-year-old Ivanovic, who has slipped to 11th in the world, was buried under a deluge of unforced errors.
"When I saw the draw I thought I could beat her," said Safarova after knocking out the 10th seed.
"But you never know what she's going to bring."
Ninth seed Flavia Pennetta was the first of the top 10 players to fall in Tokyo, bundled out unceremoniously by fellow Italian Roberta Vinci 6-1, 6-2.
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