The first two quarterfinals at the inaugural bett1open both went down to the wire, as Alizé Cornet upset No.6 seed Garbiñe Muguruza 4-6, 6-3, 7-6(5) after saving one match point, and No.5 seed Belinda Bencic held off Ekaterina Alexandrova 6-4, 4-6, 7-6(4).

Cornet's win puts the 31-year-old into her 25th career semifinal - but the first on grass. Previously, her deepest run on the surface was a quarterfinal showing at Eastbourne 2019, though she also pulled off a memorable upset of Serena Williams at Wimbledon 2014.

It is also Cornet's third Top 20 win of 2021 following her defeats of Elise Mertens in the second round of Charleston and Bianca Andreescu in the second round this week. The Frenchwoman has now defeated at least three Top 20 opponents in eight separate seasons, including every year since 2017.

Cornet had lost both of her previous completed matches against Muguruza, though their only encounter since 2014 saw the Spaniard retiring after five games in the 2017 Brisbane semifinals. Here, the World No.63 competed with tremendous fortitude and balanced keeping her own game watertight with giving Muguruza awkward angles and spins. She finished with 19 winners to 20 unforced errors, compared to Muguruza's 34 winners and 29 unforced errors.

Remarkably, there were only six break points over the course of two hours and 40 minutes, four of which were converted - with Cornet impressively taking her only two opportunities. After an opening exchange of breaks as both players settled into the match, the first two sets would be decided by one key game.

In the first, Cornet threw in a loose game of three unforced errors and a double fault at 2-2. Muguruza did not relinquish the lead, closing out the set with a delicate dropshot putaway.

But Cornet rebounded at the start of the second set as Muguruza lapsed into error herself, leaping out to a 3-0 lead and successfully preserving it to force a decider. Both players would struggle with consistency when it came to opportunities on return, but showed razor-sharp clutch instincts when it came to shutting the door on half-chances on their own serve.

Though Muguruza took an off-court medical timeout ahead of the third set, she successfully passed Cornet's attempts to test her movement on resumption, and there were no break point opportunities through the first nine games of the third set. Indeed, it was the former World No.1 who made the first breakthrough, chasing down a dropshot to flick a fabulous winner to reach match point at 5-4.

But Cornet came out on top of a bruising baseline exchange to save it after Muguruza netted a forehand. In the ensuing tiebreak, Muguruza got off to a nightmare start, committing five unforced errors in the first seven points to fall behind 1-6.

The two-time Grand Slam champion wasn't about to lose quietly, and saved the first four match points with three clean winners and a bruising backhand that was as good as one, sending Cornet on to the grass as she desperately attempted to retrieve it. But Cornet's defence paid dividends on the fifth: another pulsating rally ended with Muguruza tapping a dropshot attempt into the net.

"It was a long match with a lot of emotion, especially in the tiebreak," said Cornet afterwards. "I can't believe I made it at the end. She's a champion, she never gives up. I should have gone for a it a bit more, I was waiting for a mistake and I was a bit tight - it's normal. But I was very resilient too, I was always behind in the score in the third set but I kept grinding, I kept fighting to the end and it's a really nice victory.

"I had a really tough clay season, I couldn't play well and I don't know why - but to play well on grass, it's unexpected but beautiful."

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Bencic returns the favour for Alexandrova revenge

Resilience was also key for Bencic, who had lost two of her previous three encounters with Alexandrova - including their only previous grass meeting at Eastbourne 2019, and their most recent clash in Stuttgart this year.

Here, the pair committed fully to pure first-strike tennis in a match that featured few extended rallies. When both were serving at their best, the quality of their deliveries racked up easy points: Alexandrova racked up 15 aces, taking her season total to 168, but Bencic wasn't far behind with nine aces.

But any serve that landed in the opponent's strike zone was liable to be smacked away by the returner, either to gain the upper hand or for a clean winner. The Alexandrova second serve proved to be a key shot. The Russian went up a break twice in the first set, but couldn't find her first serve when it mattered - and was able to win only one of her 12 second serve points.

Aptly, the last of those was on set point, as Bencic sealed a run of four consecutive games by hammering a return straight at Alexandrova's feet.

Alexandrova improved the efficacy of her second serve in the second set, winning six of 12 points. By contrast, a visibly frustrated Bencic paid the price for consecutive double faults which paved the way to an early break, a first serve percentage that plummeted to 32% and a ratio of five winners to 11 unforced errors.

Ricocheting a sequence of breathtaking backhand winners down the line, Alexandrova would be unable to take three set points on the Bencic serve at 5-3 - but bounced back to serve the set out to love.

Both players remained firm behind their deliveries throughout the decider, which saw just one break point - in the eighth game, saved by a Bencic ace. The Swiss player came within two points of the match in the subsequent game, but four Alexandrova aces were too much to overcome.

But in the ensuing tiebreak, Bencic rose to the occasion. She ended a rare pair of lengthy rallies with forehand winners to win the first two points and never relinquished her lead, sealing her second match point as Alexandrova put an attempted wrong-footer wide.

"I definitely don't like playing her," said Bencic afterwards. "There's not so much rhythm, she's very aggressive player, it's tough to stay in the rally. I would say I'm more relieved [to get through]. It didn't even feel like a third set tiebreaker - it was really about serving and returning. I'm really happy I stayed tough today."

Bencic, who let her frustration show during the second set in particular, also spoke about channelling her emotions into her game.

"I have to get mad," she said. "When I'm mad, I play better, I'm just hitting the ball. So I'm trying to get mad on court."

Getting mad has moved Bencic into her second semifinal of the year following Adelaide in February, and fifth of her career on grass. Alexandrova, meanwhile, falls to 1-4 in quarterfinal matches in 2021.