Paris, France (SportsNetwork.com) - Ana Ivanovic and Lucie Safarova won quarterfinal matches Tuesday at the French Open.

Ivanovic, the 2008 women's champion, rolled to a 6-3, 6-2 victory over Elina Svitolina of the Ukraine and will next play Safarova, who followed her monumental upset of defending champion Maria Sharapova with a 7-6 (7-3), 6-3 triumph over Spain's Garbine Muguruza.

There was little drama for Ivanovic, who needed just 75 minutes to advance to her first Grand Slam semifinal since winning her lone major championship seven years ago on the famed red clay at Roland Garros.

"Obviously, I'm very thrilled to be in my first semifinal at a Grand Slam since 2008," said Ivanovic. "It's been a long road and hard work. And you can't take any victory for granted, let alone a quarterfinal. It's not every day that you reach that -- it's been a long time. So I am really pleased."

The seventh-seeded Serb ripped 37 winners, including 28 on a dominant forehand side, while converting four of her five break-point opportunities. Svitolina, in her first Grand Slam quarterfinal, managed only one break of serve and hit only eight winners in falling to 0-7 lifetime against Ivanovic.

"It was tough conditions, obviously for both of us," said Ivanovic. "It was very, very gusty. I really tried to just execute my game plan and tried to move my feet more because in windy conditions that's just what you have to do."

Ivanovic ascended to the top of the women's rankings after her triumph in the French capital in 2008, but it's been mostly a struggle since. Only twice in the last 27 Grand Slam tournaments has she even reached the quarterfinals -- falling in the round of eight at the 2012 U.S. Open and at the same stage in the 2014 Australian Open.

This week's run has featured a trio of three-set matches, including two when she had to rally after dropping the first set. She'll next have to face an opponent that ended her 2014 French Open stay.

Safarova beat Ivanovic last year in the third round at Roland Garros, a 6-3, 6-3 triumph. The pair also met in the second round in 2008, a 6-1, 6-2 romp for Ivanovic on her way to the title.

"Lucie is a great player. She's showed that many times," Ivanovic added. "She had a great match against Maria, and she won Doha beating Azarenka. And last year I lost in straight sets to her here. She's doing great, and she obviously deserves her spot here. So it's going to be a tough matchup for me."

Overall, Safarova owns a 5-3 advantage in the all-time series.

Safarova advanced to her second career Grand Slam semifinal. She also made the final four last year at Wimbledon, falling to eventual champion Petra Kvitova.

Muguruza was playing in her second straight French Open quarterfinal, but again could not advance farther. She lost to eventual champion Sharapova in three sets last year and on Tuesday had no real answer for Safarova's sharp play.

Safarova won the tiebreak, converting a minibreak on a 26-stroke rally, after neither player managed to break serve in the first set. The Czech failed on six chances to break in the first set, then came up with a pair of breaks in the second and finished the match with a backhand winner.

The remaining two quarterfinal matches will take place Wednesday.

Two-time French champion Serena Williams will take on 2012 runner-up Sara Errani and Timea Bacsinszky of Switzerland will meet Belgium's Alison Van Uytvanck.

Williams, the 2002 and 2013 winner, has had to rally from a set down in each of her last three matches, including Monday's 1-6, 7-5, 6-3 decision over fellow American Sloane Stephens. Errani, who lost to Sharapova in the 2012 final, will play in her fourth straight French quarterfinal.

Bacsinszky, seeded 23rd, knocked off the fourth-seeded Kvitova on Monday in the fourth round to reach her first career Grand Slam quarterfinal. Van Uytvanck is also making her major championship quarterfinal debut, but has yet to face a seeded player in her first four matches.