Belinda Bencic put her friendship with Donna Vekic to one side as she booked her place in a Grand Slam semi-final for the very first time at the US Open. The world No 12 held her nerve to win in straight sets in one hour and 40 minutes on Wednesday, 7-6 (7-5) 6-3 to set up a last four encounter against either Bianca Andreescu or Elise Mertens. It was Vekic who produced more winners and fewer unforced errors during a tense opening set at Arthur Ashe Stadium, and the world No 23 was even the first to break serve. But Bencic, who knocked out defending champion Naomi Osaka in the previous round, responded immediately to take it to a tie break, where two dropped points on serve proved pivotal for the Croatian. Bencic then took command of the match in the second set, committing just four unforced errors compared to 17 in the first. Vekic fired 28 winners during the match but failed to save critical break points against her, as an elated Bencic reached a new milestone in an injury-plagued career. Vekic had defeated her opponent in one major already this year – a third round win at Roland Garros – and she showed her courage in saving four of six break points in the second set. But she was ultimately worn down by her opponent with 12 unforced errors taking their toll. Bencic eventually secured the break after a delicious drop shot return of serve in the seventh game, and on her third match point, the Swiss secured the milestone win. The victory over Vekic will put Bencic in the top 10 of the world rankings. "Sometimes you all take it a little bit for granted," said the 22-year-old. "When you canвЂ™t play you miss it so much. "For me itвЂ™s a perspective change and I am enjoying playing tennis so much now."