Former world number one Ivanovic looked in danger of a shock defeat when 17-year-old Oudin, ranked 68th, ripped though the first set of their match.
The Serb had trouble with her ball toss early on but recovered her composure to storm back in the next two sets.
"I didn't start so well and I had lots of unforced errors and lots of double faults," said Ivanovic, who now plays Melinda Czink of Hungary.
"But after the first set I just tried to talk to myself and just try to convince myself I have to be aggressive and play the way I should play and not wait for mistakes."
Ukrainian qualifier Kateryna Bondarenko set up a meeting with second seed Serena Williams after she crushed Magdalena Rybarikova of Slovakia 6-2, 6-2.
World number one Dinara Safina begins her title bid on Tuesday with a second-round meeting with Roberta Vinci of Italy.
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