France had a large surplus of possession for most of the match and an advantage of territory, but for a long period through the middle of the match seemed incapable of finding a way to score against stoic Italian defence.
The turning point in the match came with the penalty try when Italy infringed at a scrum near their line and Silvia Turani, singled out as the offender, was sent to the sin-bin.
France cashed in immediately on their numerical advantage with a try to Laure Touye, then Grisez touched down in the 68th and 70th minutes to complete a rare World Cup triple and make France's win conclusive and impressive.
"We are so happy to play a semifinal next week," France captain Gabrielle Vernier said. "I'm so proud of the girls. It's been a tough few weeks and we proved when are one of the best teams. It's a dream come true and I hope for the best for the team."
France should have scored in the 45th minute when they had a three-player overlap but cut back inside. They also should have scored two minutes later but Charlotte Escudero dropped the ball over the line. France seemed set to be denied by the Italy defence and relied on penalties to extend their lead after Grisez's early try.
But the floodgates opened with the penalty try and France will be formidable in the semifinals, especially on the basis of their defensive performance. They have conceded just 21 points in four games.
Italy were playing in their first World Cup quarter-final and may use their experience in New Zealand as a springboard to better things.
"We are happy to be here and to get to the quarter-final but we need to start from this and improve in the next year - maybe in the next World Cup and get to the semifinal," captain Elisa Giordano said.
- AP