Mauresmo, unseeded and ranked No. 33 in the world after being hampered by nagging injuries this year, will face top-seeded Anna Chakvetadze in the semifinals Friday.
"I am definitely very happy about this one,'' Mauresmo said. "I thought I mixed up pretty well tonight and was really solid not giving her many free points and making her work for every point.''
Szavay, ranked No. 14 in the world, saved two match points in the 10th game before Mauresmo finally broke her in the 12th to win.
"I got a little tight on that moment,'' Mauresmo said. "I guess I need to get used to being back again in these kinds of situations. But after losing that game I really regrouped really well, played a good service game and then put a lot of pressure on her service game. I tried to learn from a couple of games ago and do much better next time.''
Szavay, the Pilot Pen runner-up last year, said Mauresmo's style of play gave her trouble.
"She was serving well I think and she has a great slice, which I couldn't really handle,'' Szavay said. "I was missing a lot and couldn't move really well. She was good today.''
Chakvetadze defeated Sorana Cirstea of Romania 6-3, 6-3 in her quarterfinal match to advance to her third semifinal of the year on the WTA Tour.
"It was a little tough conditions,'' Chakvetadze said. "It was too hot. In the beginning of the second set I felt a little dizzy, but then I was fighting until the end. That's why I won.''
There were two upsets in the women's draw.
Second-seeded Daniela Hantuchova lost 3-6, 6-4, 6-4 to Alize Cornet, who played with an injured left quadriceps muscle.
"It's good because I won the match without playing my best level,'' Cornet said. "So, it means I can do better.''
It was a tough day for Hantuchova, who also lost her doubles match with Lindsay Davenport to Russians Anastasia Rodionova and Galina Voskoboeva 6-3, 1-6, 11-9.
But Hantuchova, who is coming back from a foot injury, said she was pleased with the way she played in New Haven.
"This was a very important week for me,'' she said. "I don't think I could have asked for a better week before the U.S. Open.''
In other action, Caroline Wozniacki of Denmark defeated third-seeded Marion Bartoli 6-4, 6-0.
"I played really well today,'' said Wozniacki, who will face Cornet in the semifinals. "In the second set I just fought one point at a time. Everything was going my way.''
Bartoli, ranked No. 13 in the world, is now 0-3 against Wozniacki.
"She is a really consistent player,'' Bartoli said. "She doesn't give you any points, especially on hardcourts. She just played better than me today.''
In the men's draw, top-seeded Fernando Verdasco of Spain dedicated his 6-2, 7-6 (4) quarterfinal win over Mischa Zverev to the victims of Wednesday's Spanair jetliner crash. Authorities said 153 people died in the crash at Madrid's Barajas Airport.
"I want to dedicate my victory today to all the victims and all the families of the victims in the flight in Madrid yesterday, and send them all of my support and everything of me that I can help for them,'' said Verdasco, who lives in Madrid. "It is my hometown and when this thing happened I felt so bad yesterday and today.''
Verdasco, ranked No. 13 in the world, advanced to his fourth ATP Tour semifinal of the season and will face eighth-seeded Mardy Fish, a 6-3, 7-6 (4) winner over fellow American Jesse Levine.
Qualifier Luka Gregorc of Slovakia also advanced to the semifinals, defeating seventh-seeded Andreas Seppi of Italy 4-6, 6-4, 7-5. He will play sixth-seed Marin Cilic of Croatia, who advanced by defeating fourth-seeded Russian Igor Andreev, 6-3, 6-2.
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Mauresmo holds off sixth-seeded Alize Cornet
