The United States capitalized on Colombia goalkeeper Catalina Perez's dismissal to earn a 2-0 win and set up a women's World Cup quarter-final against China, while England continue to build up a head of steam after coming from behind to beat Norway.

England's reward for fighting back in sweltering conditions to record a 2-1 victory is a last-eight tie against hosts Canada in Vancouver on Saturday.

The United States will face China a day earlier in a repeat of the 1999 final but they had to work for their win at the Commonwealth Stadium in Edmonton and only took control of the game with the sending off of Perez after half-time.

Despite a series of unconvincing displays, U.S. coach Jill Ellis was happy with the way her team were finding a way to win.

“This is the World Cup, I am really satisfied with advancing,” said Ellis. “It is about finding a way. I thought we stroked the ball around pretty well at times. So I am pleased with where we are."

The game turned the Americans' way shortly after half-time when Alex Morgan was brought down just inside the area by Perez, who was then sent off.

Abby Wambach missed the penalty but the opening goal arrived in the 53rd minute when substitute goalkeeper Stefany Castano failed to deal with a near-post shot from Morgan.

The United States doubled their advantage 13 minutes later when Megan Rapinoe was brought down in the box and this time Carli Lloyd was given the penalty-taking duties and made no mistake from the spot.

United States midfield duo Rapinoe and Lauren Holiday picked up yellow cards on Monday and will miss the game against China. That game will be a repeat of the 1999 tournament's final, which the Americans won in a penalty shootout on home soil.

Wambach could find herself in trouble with FIFA after suggesting the French referee may have deliberately chosen to give yellow cards to team mates on the verge of suspension.

"I don't know if they were yellows. It seemed like she was purposefully giving those to the players she knew were sitting on yellows. I don't know if it was just a psychological thing, who knows?" Wambach told reporters.

Earlier at Landsdowne Stadium, where the temperature hovered around 40 Celsius (104 Fahrenheit) in the first half, Norway's Solveig Gulbrandsen got her head to a corner at the near post and flicked the ball in off the bar to give her team the lead in the 54th minute.

England, who lost their group opener to France but have now won three in a row, equalized from a corner in the 61st minute when captain Steph Houghton outmuscled two defenders to score with a fine header of her own.

Defender Lucy Bronze then blasted in the winner in the 76th minute to book England's spot in the quarter-finals. ”We have an excellent record against this Canada team ... the momentum we got from this game will put us in a great place going into the quarter-final," said England coach Mark Sampson.

The remaining last-16 game takes place on Tuesday with Japan taking on the Netherlands in Vancouver. The winner of that game will play Australia for a place in the semi-finals.

By Simon Evans