Home player Amelie Mauresmo, No. 16 seed, became the biggest upset of the day, crashing out after a 6-4, 6-3 defeat by Anna-Lena Groenefeld of Germany.
Ivanovic's title defence had a bumpy start as the eighth seed had to fight a tiebreaker before watching Errani commit two uncharacteristic unforced errors to end the 72-minute first set.
With much more confidence in the second, she did not waste much time to close out the contest on third match point.
The 21-year-old will now play Thailand's Tamarine Tanasugarn or Camille Pin of France for a place in the third round.
Ivanovic, who missed last week's Madrid Open because of a knee injury, had the problem area taped when she walked onto court, but it did not hinder her in the early exchanges as she moved 3-1 ahead.
Then she was struggling a bit with her serves and a gritty Errani. While trailing at 5-4, the champion nailed a series of brilliant forehand winners to force a tiebreaker before winning it convincingly.
"Obviously I expected a tough match. I knew I had to work hard for my points today, and I'm happy I did that," said Ivanovic.
"I think this match is going to be a good test, but I feel good. I had really good practice sessions from the beginning of the year. I was working really hard.
"So even though I had some time off during the Madrid tournament, I feel like it takes only few days to get back in shape. I feel very fit," she said.
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2020-09-15
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