Ivanovic came back from a set down to win 4-6 6-3 6-3 - the Serb's first ever victory over Williams in five attempts.
"It's amazing," said Ivanovic. "Honestly, I went on the court and I just wanted to play the best I could. I'm so thrilled."
The 14th seed faces Eugenie Bouchard or Casey Dellacqua in the last eight.
Williams, the world number one and reigning French and US Open champion, had been tipped by some to complete the Grand Slam of all four major titles in 2014.
That will not now happen after the 32-year-old was well short of her best against a rampant Ivanovic on Rod Laver Arena.
Ivanovic, 26, is a former world number one and 2008 French Open champion, but since then she has reached just one major quarter-final at the 2012 US Open.
A 0-4 record against Williams gave little cause for optimism either, but from the outset Ivanovic was able to threaten the American's usually impregnable serve.
The Serb fashioned four break points in the opening set, converting one, but was broken twice as Williams edged it.
Ivanovic took over from that point, her once fragile serve holding up well as Williams appeared to struggle with her movement, and she did not face another break point.
Williams was warned for a time violation when serving to stay in the contest and managed to save two match points , but Ivanovic closed it out nervelessly with a love hold after one hour and 56 minutes.
"I was very consistent," added Ivanovic.
"It's not easy playing such a champion, but she's also just a human and I know she has lots of pressure too.
"I just went out there swinging and I think I did that really well."
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