The Dutch, deserved victors in intense heat at the Stade du Hainaut, will face the winners of Saturday's other quarter-final between Germany and Sweden, who play later in Rennes.
Italy, who have never gone beyond the last eight, had the better of the chances in the first half but the European champions stepped up their game after the break and both goals came from quality set-piece deliveries from Sherida Spitse.
Defending World Cup champions the United States will face England in the opening semi-final on Tuesday in Lyon with the second semi on Wednesday.
The Netherlands' left-sided playmaker Lieke Martens was passed fit despite suffering a foot injury while celebrating a goal in the previous round.
With the venue only a two-hour drive away from the Dutch border, the 22,600 crowd was mostly bedecked in Orange in the bright sunshine.
But despite those boosts, the Dutch initially struggled to create openings against an Italian defence well marshalled by captain Sara Gama.
The Azzurre had the first real chance when Barbara Bonansea's flick-on found Valentina Bergamaschi in the area but the midfielder's lob was too easy for Dutch keeper Sari van Veenendaal.
Bergamaschi had another chance when, after a smart interchange won her space in the box, she scuffed her shot and then moments later Valentina Giacinti pulled her shot wide from a promising position.
The Dutch coach Sarina Wiegman clearly took advantage of the break to address their problems and it was a very different approach after the interval.
The introduction of Lineth Beerensteyn for the out-of-sorts right-winger Shanice van de Sanden also helped the Dutch step up the tempo but when the breakthrough came in the 70th minute it was from a set piece.
Spitse, from wide on the left, whipped in a fine, high cross and the towering Miedema timed her run and jump perfectly, beating Laura Guiliani with a deft, glancing header.
Ten minutes later the game was put beyond the Italians when Spitse, this time from the right, delivered a flat cross which defender Van Der Gragt met with a firm header.
Italy had nothing left in the tank and it was cruise control from then on for the Dutch, who will now fancy their chances of reaching the final for the first time.
"I didn't expect to be in the semi-finals of this World Cup," said Miedema.
"We've been complaining that we're not playing the best football but in the end we're in the semis. We've done amazing and we can be really proud," she said.
An emotional Italy coach Milena Bertolini said her team had achieved more than just a run to the last eight.
"The women’s game has been discovered and appreciated back home, so it’s a big deal. I believe the girls have a greater confidence and awareness of what great players they are," she said.
"They need to be proud of themselves. The way they played and approached matches and their passion, they’ve shown people back home that football can be a sport where you have enjoyment, helping one another, unity and all these values. I think that’s why the public have fallen in love with this team."
(Reporting by Simon Evans; Editing by Christian Radnedge and Toby Davis)
