MADRID, Spain -- Belinda Bencic of Switzerland notched her second straight upset of World No.1 Naomi Osaka this season, overcoming the Japanese star 3-6, 6-2, 7-5 on Thursday to reach the semifinals of the Mutua Madrid Open.

World No.18 Bencic stared down a 5-4 deficit in the deciding set, but broke Osaka when the top seed served for the match, en route to clinching the final three games of the tilt and garnering a hard-fought two-hour and 10-minute victory.

"[Osaka] was putting me under a lot of pressure and I didn't catch a very good start on the start of the match," Bencic told the press, after the match. " In the second set, I just tried to play a little bit more aggressive, more brave, tried to push her more and go for my shots more. I feel like that helped a lot."

As it happened: How Bencic came back from the brink to stun No.1 Osaka in Madrid

"I also started serving better," Bencic added. "I don't know how I turned it around. I just tried to hang in there and keep, and play for every ball and somehow it turned around."

Bencic had also defeated Osaka in their most recent match at the BNP Paribas Open in Indian Wells in March, where the Swiss player ended Osaka’s title defense in the round of 16. Bencic's latest upset improves her 2019 win-loss record against the Top 5 to a staggering 5-0.

"For sure it helped that I had played [Osaka] before," Bencic admitted. "I know how the ball feels. I feel like people underestimate who are watching on the TV. Her ball is very heavy, you cannot see, but she puts you under a lot of pressure with all her shots, so you don't have time to construct the rally and to play around."

In the final four in Madrid, Bencic will now face 2016 and 2017 Mutua Madrid Open champion Simona Halep. The No.3 seed from Romania got past No.9 seed Ashleigh Barty in two tough sets in an earlier quarterfinal on Thursday. Bencic defeated Halep in Dubai earlier this year for her second win in their three meetings, en route to winning that title.

"I think [Halep is] a very solid player, a great player," said Bencic. "She's been on the top for very long time now and the clay specialist. So, it will be for sure a tough match. I have reached more again than I imagined in this tournament and, in that case, I will just play very freely and very brave and hope to play a good match tomorrow."

In the first set, Osaka claimed the initial break to lead 3-1 before Bencic broke back immediately, as the two players were taking risks on both serve and return. Osaka used her powerful shots to get through a close game at 4-3, as the velocity of her strokes caused two shots which clipped the netcord to continue over to Bencic’s side for winners.

Bencic had trouble rebounding from that turn of events in the following game, firing a double fault and a backhand miscue to slide from 30-15 to break point. The Swiss player blasted a second double fault of the game to drop serve, ceding a pivotal lead to Osaka at 5-3.

Serving for the set, Osaka slammed two stellar serves to open up a 30-0 lead before a long return by Bencic gave the top seed triple set point. Bencic blasted a backhand winner to save one of those chances, but Osaka converted her second opportunity with her fourth ace of the set.

However, Bencic continued to stay with Osaka, and took her chance early in the second set, fending off three break points in her opening service game, then using deep returns to break Osaka and lead 2-0. A winning volley put Bencic up 3-0, giving her new life in the match.

Osaka used some dazzling crosscourt hitting to claim the break back and get to 3-2, but a stunning, precise forehand pass by Bencic on the second point of the next game proved to be a tipping point, as the Swiss player reeled off eight straight points from there to break Osaka and consolidate, swiftly grabbing a 5-2 lead.

Bencic extended her streak to ten straight points before Osaka could stop the run, and a wide backhand miscue by the World No.1 gave Bencic set point. There, Bencic slammed a backhand return winner to wrap up the second set, in which the Swiss player had ten winners to just three unforced errors.

The final set was wide open and unpredictable, starting with both combatants staving off break points in their respective opening service holds. However, it was Osaka who used ferocious forehands to ease to a love break of Bencic in the fifth game and open up a 3-2 lead.

Osaka then had to work extremely hard to consolidate that hold, needing an 11-minute, six-deuce game to get to 4-2, saving a pair of break points in the process. Osaka’s subsequent service hold was far less complicated, as she used a duo of down-the-line backhands to reach triple game point, before holding for 5-3 with a strong serve.

But Bencic fought through a tough service game of her own, punching a forehand winner to hold for 5-4 from deuce. Osaka then served to wrap up the win, but Bencic suddenly caught fire with outstanding returning. Bencic quickly reached triple break point, and she converted the first opportunity with a return winner, leveling the clash at 5-5 in the decider.

Bencic struck another forehand winner to hold for 6-5, and, all of a sudden, Osaka had to hold serve to prolong the match. More big Bencic returns caused problems for Osaka, and the unseeded Swiss found herself with two match points. On the first match point, a backhand error by Osaka ended the affair, and Bencic had executed an eye-opening comeback to squeak past the World No.1 into the semifinals.