No.3 seed Emma Raducanu delivered a solid performance to defeat Ana Bogdan 6-4, 6-4 in one hour and 30 minutes and reach the last eight of the Transylvania Open.

She was followed on court by No.1 seed Simona Halep, who came through 6-4, 6-2 over Varvara Gracheva despite a back injury, and No.2 seed Anett Kontaveit, who defeated Alison Van Uytvanck 6-3, 6-4 to keep her hopes of qualifying for the Akron WTA Finals Guadalajara alive.

It is the freshly crowned US Open champion's second quarterfinal in her sixth Tour-level main draw and the first she has contested as a seed. The result takes her overall win-loss record this year to 25-8.

"It's definitely taking me some time to find my feet still," said Raducanu afterwards. "I'm just taking some learnings from every match that I play. I don't think I'm the finished product yet."

Against Bogdan, Raducanu displayed some of the razor-sharp scoreboard management that had seen her win in Flushing Meadows as a qualifier without dropping a set in 10 matches. The Briton won three out of four multi-deuce games, and withstood a putative comeback in the second set as Bogdan pegged her back from a break down.

Key shots and decisive moments: Raducanu's serve was crucial. She landed 69% of her first serves and won 87% of those points, with her slider out wide repeatedly gaining her free points. As at the US Open, the 18-year-old found a balance of first-strike aggression and scrambling athleticism to out-maneouvre Bogdan, whose overall error count outweighed her flashes of brilliance.

The first set was decided in its opening games. Raducanu fended off three break points to hold, then promptly found a booming backhand to capture Bogdan's serve to love - the sole break of the set. The Romanian's best passage of play came in winning a trio of consecutive games in the second set to surge from 0-2 to 3-2, but Raducanu regained control after finding another superb backhand to rebreak for 4-3.

What's next for Raducanu: An intriguing quarterfinal clash against fellow 2002-born peer and No.6 seed Marta Kostyuk, who eased past Mona Barthel 6-4, 6-4.

The Ukrainian was the first of their generation to break through after reaching the third round of the 2018 Australian Open as a 15-year-old, and is currently perched at World No.55 after a season that has included a semifinal showing in Abu Dhabi and a fourth-round run at Roland Garros.

It will be the first pro meeting between the pair, who did not play each other at junior level either. However, they did contest two Tennis Europe matches in the most nascent stages of their careers. Raducanu won 6-1, 6-3 in the third round of the U12 tournament in Auray, France on indoor hard courts in 2014, going on to make the semifinals. A year later, Kostyuk avenged the loss 6-1, 6-1 in the second round of the U14 tournament in Hasselt, Belgium on clay, going on to win the event.

Halep fights past injury to defeat Gracheva

Former World No.1 Halep's season has been disrupted by a succession of injuries, a pattern that unfortunately continued at her home tournament.

A calf tear forced the 30-year-old to withdraw from Rome, and eventually miss Roland Garros, Wimbledon and the Tokyo Olympic Games. Today, her back was the problem.

"The back got blocked and the pain is really big," Halep said in the on-court interview. "You cannot really bend much and you cannot move. But sometimes you are used to the pain, I had this before many times, and I just wanted to continue and finish this match. It's good that I won this match, I don't know how."

World No.81 Gracheva, 21, came out of the blocks firing, committing to a strategy of all-out aggression to hit through Halep. This garnered the Russian, who reached her first WTA semifinal at the Chicago Women's Open in August, a number of spectacular winners - which were unfortunately outweighed by a plethora of unforced errors.

As Halep's movement became more visibly compromised, Gracheva's shots became increasingly wild. Halep was able to batten down the hatches and deliver a series of service winners to retain control of a one-sided second set.

"This is my main principle and main goal, to never give up, so I do what I can," she said afterwards. "Sometimes even if it's painful, if it hurts, you have to continue when you know it cannot be worse. It's just a back block - I've had it before and I know how to manage it, I think. I just keep playing. Sometimes I lose these matches, sometimes I stop - but today I felt being at home I had to fight more."

The next challenge for Halep will be preserving her 100% record at WTA main draw level against fellow Romanians against No.105-ranked wildcard Jaqueline Cristian.

Kontaveit extends indoor streak, stays in hunt for WTA Finals

Kontaveit's battle with Van Uytvanck was a clash of two active indoor winning streaks. Nur-Sultan champion Van Uytvanck, who has lifted four WTA trophies indoors, had won six in a row under a roof; Kontaveit, winner in Ostrava and Moscow this autumn, had 11 straight victories under her belt.

It was the Estonian who extended that to 12 with another stellar performance. Van Uytvanck had led their head-to-head at pro level 2-1, and looked to be building on that when she took an early break lead for 2-1.

But Kontaveit immediately broke back to love, and kept the pressure on to capture the Belgian's serve for 4-3 in the second set as well. Only then did she falter again behind her own delivery - but strong returning regained her the advantage immediately, and the 25-year-old made no mistake serving out the win.

Kontaveit needs to win the title in Cluj-Napoca this week to overtake Ons Jabeur and secure the last spot in the WTA Finals field. She will next face No.8 seed Anhelina Kalinina in the quarterfinals. Kalinina is one of three Ukrainians in the last eight, along with Kostyuk and qualifier Lesia Tsurenko, who faces Rebecca Peterson. This marks the first time that a WTA quarterfinal line-up has featured three Ukrainians.