Schiavone had won all four prior meetings but this one was by far the closest, with Razzano looking headed for victory up 3-2 in the third set, but Schiavone finishing fast with four games in a row.
Schiavone is now through to her fourth WTA quarterfinal of the year, having already been to the quarterfinals of Acapulco (falling to Carla Suárez Navarro in three sets), Marrakech (where she went on to capture her sixth WTA title) and Birmingham (falling to Daniela Hantuchova in three sets).
Three seeds were in action but only one managed to make it through, that being No.3 seed Anastasia Pavlyuchenkova, who had some early trouble against Lee Ye-Ra - she fell behind 4-1 in the first set - but then won nine straight games and eventually cruised past the South Korean wildcard, 64 61.
"It wasn't easy - I was a bit sluggish at the beginning today, and I wasn't very happy with myself," Pavlyuchenkova said. "But I'm happy I pulled the first set through and won in straight sets. I have to say she was fighting until the end, though - the second set score doesn't show how tough it was.
"I definitely have to raise my level in the next match. It's only going to get tougher now."
The other two seeds in action didn't manage to regroup and move through, though, with Irina-Camelia Begu winning nine straight games from 3-4 in the first set to beat No.6 seed Julia Goerges, 64 60, and Vera Dushevina blasting 10 aces to win a tight two-setter against No.8 seed Annika Beck, 63 75.
"I played really well today," Begu said. "I was really strong from the baseline, and I tried to keep a high percentage of first serves in. And I really enjoy playing this tournament - it's really nice here.
"It hasn't been such a good year for me, so I'm just trying my best every match to improve."
In the only all-unseeded battle of the day, Lara Arruabarrena won a see-saw three-setter against Alexandra Dulgheru, 61 36 64. Dulgheru looked like she was clawing her way back into the match during the second half - she won the second set and, after falling behind 4-2 in the third, ground out two games in a row to even the decider at 4-all. But Arruabarrena held then broke one last time to win.
"It was a very tough match - the weather was very hot, and even though I was playing well, she was playing well too," Arruabarrena said. "I was playing aggressive with my forehand today, and I think I was just a little bit more aggressive in the important points, which is what made the difference.
"It's tough playing a friend. Alexandra and I know each other very well. Sometimes we go shopping together or go for dinner. But I just had to focus on the match and not that I was playing a friend."