The win over Bournemouth was a hard fought one.
Adam Smith's own goal proved to be the difference for the hosts, as he inadvertently headed past Cherries goalkeeper Mark Travers from a superb delivery.
The home team created the majority of the goal scoring chances and Eddie Howe's side deserved it.
The draw will take place on Thursday night.
Goalkeeper Nick Pope, full-back Trippier, and forward Wilson, who were all part of the England World Cup squad, were included in the starting XI by Howe.
Both Switzerland and Brazil appeared to be close to full strength for the first time in over a month when the two teams met.
Wilson's effort was ruled out for offside and Trippier's effort was also ruled out in the first half as the teams played out a goalless draw.
Bournemouth will count themselves a little unfortunate after failing to make the most of their few clear-cut opportunities.
Dominic Solanke's late effort was blocked by the goalkeeper, after he was forced into a good save by substitute JackStacey.
It was the fourth quarter-final appearance in the last five years forNewcastle, who lost in the 1975-76 season.
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