Veteran USA striker Abby Wambach insisted her side were "bound for glory" after a 2-0 win over New Zealand kept the defending champions on course for a third straight Olympic football title.
Wambach fired the United States into an early lead at St James' Park, the home of English Premier League club Newcastle, on Friday as the holders booked their place in the last four.
But it was not until three minutes from time, when Sydney Leroux added a second goal, that victory was secured.
The Americans will now face either hosts Great Britain or Canada, who play later Friday, in the semi-finals.
"This team is bound for glory," said Wambach. "It might not look pretty in every second of the game, but we get it done."
Wambach paid tribute to New Zealand by saying: "They are very physical. They're one of the most improved teams in this tournament in the last few years. You have to give them credit.
"The workrate they have is amazing, but they couldn't save it in the second half as they got a bit tired.
"They have a fantastic future and they're a great team."
Meanwhile France marked their first appearance at an Olympic women's football tournament by reaching the last four following a 2-1 win over Sweden at Glasgow's Hampden Park.
Sweden took the lead in the 18th minute when Nilla Fischer deflected in a Marie Hammarstrom corner off her shoulder but France equalised 11 minutes later through Laura Georges's header from a corner.
France then went ahead shortly before half-time courtesy of Wendie Renard's powerful shot.
But that they won in normal time was down to goalkeeper Sarah Bouhaddi, who made a superb one-handed save to stop a Fischer volley that seemed destined for the top corner.
Victory gave France a measure of revenge for their defeat by Sweden in the third place playoff at last year's World Cup.
"Sarah made a great save at just the right moment that allowed us to continue into the semi-finals," said France coach Bruno Bini.
"A goalkeeper can lose you a match, but there are a very few that can win you a match."
France will now play either Brazil or world champions Japan in the first semi-final at London's Wembley Stadium on Monday.