Emma Navarro reached her first career grand slam semifinal on Tuesday, defeating Paula Badosa 6-2, 7-5 in the first women's quarterfinal of the US Open on Monday.Video above: Coco Gauff’s US Open defense ended by NavarroThe American scored the victory in 1 hour and 12 minutes in an up-and-down matchup under the New York sunshine. She was left with a mountain to climb in the second set after going a double breakdown but rallied to stun Badosa while keeping a cool head throughout."After I got it back to 5-2 (in the second set) I kind of had a little bit of an inkling that it might be two sets," she said on the court after the game. "I just wanted to stay really tough and stick in there. And even if I did lose the second set I wanted to set the tone for the third set."Really happy with my performance today and crazy to be moving on to the semifinals. US Open, baby!"I can't see the future but today maybe I could a little bit."This was only the second career meeting between the pair, with Badosa winning their first matchup.Both players entered Arthur Ashe Stadium having already matched their best-ever grand slam performances – the last and only other time Badosa reached the quarterfinals at a major was in 2021 at the French Open, while Navarro made the last eight for the first time at Wimbledon earlier this year.It was unlikely that Navarro needed any more motivation during the match, but there was American sporting royalty in attendance inside the famous arena – nine-time Olympic champion Katie Ledecky was shown on the broadcast, keeping up with the action from the stands.Navarro set the tone early with a convincing win in the opening game before immediately stealing a march on her opponent to go up 2-0 after Badosa double-faulted on break point.A hard-hitting first set ensued, with Navarro showing off her strong serve performance that has helped her progress through the tournament. According to the US Open, she entered the match having won 64% of her points on serve and had a 69% first-serve percentage against Badosa in the first set.Badosa was plagued by mistakes in the opener, hitting 16 unforced errors to her opponent's five and serving five double faults to put her on the back foot.In a crucial eighth game of the first set, a blistering cross-court passing shot teed up set point for Navarro, which she converted at the third time of asking when a Badosa drop shot missed the line to secure the double break.Badosa came out firing to start the second set however, immediately breaking in the first game and then again in the fifth to leave the American reeling. Navarro's unforced error count climbed upward, while Badosa saw more of her first serves to find the mark.Holding serve to take a commanding 5-1 lead, the Spaniard looked poised to send the match to a deciding set, but the 23-year-old New York native had other ideas. Navarro reeled off six games on the spin to move ahead at 6-5, with Badosa looking visibly shaken after seeing her advantage evaporate.Navarro broke Badosa again for the fifth time in the match to seal her place in the next round and ensure American representation in the women's semifinal.She will take on either world No. 2 Aryna Sabalenka or 2024 Olympic champion Zheng Qinwen for a place in the final.