Simona Halep steamrolled into the Porsche Tennis Grand Prix quarterfinals on Thursday, as the No.2 seed ousted Marketa Vondrousova, 6-1, 6-3.

World No.3 Halep is still seeking her first trip to the final in Stuttgart, but her clay-court season debut proved to be a huge step towards achieving that goal as the Romanian dispatched 2019 Roland Garros finalist Vondrousova in just 56 minutes of play.

"Starting the clay court season makes me very happy and motivated, extra motivated actually," Halep told the press, after her win. "I missed playing matches. I had a few weeks without an official match and it was kind of tough when I started the match, but my mind was strong enough just to give focus on what I have to play. So, I did it great and today, it was a great match."

20th-ranked Vondrousova came into the encounter with an impressive 2-0 head-to-head lead over Halep, having notched three-set victories over the former World No.1 twice in 2019: on hardcourt in Indian Wells and on clay in Rome.

But Halep at last got on the board in their rivalry, dominating the Czech throughout their tussle. Halep never faced a break point in the affair as she moved into the elite eight in Stuttgart for the fourth time in her six main-draw showings.

"I was a little bit nervous before the match because I played twice against her and she beat me every time," Halep admitted. "I was a little bit scared of her dropshots, so [coach Darren Cahill] told me that I have to be more aggressive today, which I did, I did it well."

Halep fired 22 winners to just 13 unforced errors in the clash, putting her one victory away from matching her best-ever showings in Stuttgart: semifinal results in 2015 and 2017. 

Vondrousova used her signature dropshots to pick up a handful of points during the first few games of the match, but after a hold by the Czech in the opening game, it was all Halep in the first set as the second seed swept to a one-set lead behind sturdy, angular hitting.

Halep dispatches Vondrousova to reach QF: Stuttgart Highlights

The pair advanced on serve through the majority of the second set, with Vondrousova tightening up her game and staying with the two-time Grand Slam champion through 4-3. But in that game, Vondrousova was let down by miscues as she fell behind 0-40, and after saving one break point with an ace, the Czech double faulted on the second.

Serving for the match at 5-3, Halep had a few minor issues of her own after a double fault and a backhand error put her behind 0-30, but the Romanian steeled herself to claim the next four points and sail into the quarterfinals.

"It is important for my mind, for my game, because the clay court season is going to be very tough," said Halep. "Now this match gave me confidence that my level is high, and if I keep doing the same thing, I will be good."

Next up for Halep will be World No.34 Ekaterina Alexandrova of Russia, who upset No.8 seed Belinda Bencic, 6-1, 7-5. 

Alexandrova is now 3-3 this season against Top 20 opposition after her 81-minute victory over World No.12 Bencic. Alexandrova finds herself in her third quarterfinal of the year, in her first-ever romp through the Stuttgart main draw.

The Russian blasted 12 aces and won 87 percent of her first-service points against Bencic, as she moved to a 2-1 win-loss record against the Swiss player.

Alexandrova, like Vondrousova before her, comes into her Stuttgart meeting versus Halep with a positive head-to-head against the Romanian. Alexandrova has triumphed in two of their three previous clashes, including a 6-2, 6-1 victory earlier this season at the Gippsland Trophy on the hardcourts of Melbourne.

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No.4 seed Elina Svitolina followed Halep into the quarterfinals after she defeated a frequent rival, two-time Stuttgart champion Angelique Kerber, 7-6(4), 6-3.

Svitolina and Kerber had faced off a whopping 13 times previously, with Svitolina holding the 8-5 edge in their head-to-head. But Svitolina had won the last six of those encounters, and she continued her recent dominance in their rivalry with the hour-and-a-half win over the highest-ranked German.

Very little separated the pair during the engrossing encounter, as they had a nearly equal number of winners (26 for Svitolina and 25 for Kerber). Ultimately, it was Svitolina who garnered one more break of service and hit five fewer unforced errors than former World No.1 Kerber, maneuvering her way into the quarterfinals for the second time in her second appearance at the event.

Svitolina twice held a break lead in the opening frame, at 2-1 and 4-3, but each time, homeland hope Kerber used her fiery left-handed forehands to break back in the very next game and keep Svitolina in touching distance. The German gritted her way to a hold at 5-5, saving three break points in that game as she kept the set on track for a decisive tiebreak.

Indeed, a breaker would settle the set and the combatants refused to pull far ahead of each other through 4-4. But a double fault by Kerber gave Svitolina an edge at 5-4, and the Ukrainian punched a winning volley at the end of the following rally to lead 6-4 and reach double set point. A netted return by Kerber on the first chance gave Svitolina a well-earned one-set lead after just over an hour of play.

Svitolina’s groundstrokes held firm from there as she powered through the second set without facing any more break points. Svitolina clinched the crucial break at 2-1 after a Kerber double fault on break point, and the Ukrainian eased to victory from there, queuing up an intriguing quarterfinal showdown with No.7 seed Petra Kvitova.

Svitolina notches 7th straight victory over Kerber: Stuttgart Highlights