Belinda Bencic beat fifth-seeded Karolina Pliskova 6-3, 4-6, 6-3 to reach the semis, ensuring her return to the top 20 in the rankings.
''I wouldn't believe I win today again,'' Bencic said. ''I'm not going to the court with any expectation. I'm just trying to play. This is the mentality I have, and this is the mentality I'm going to keep having.''
Bencic's victory set up a semifinal against No. 8 seed Angelique Kerber, who beat error-prone Venus Williams 7-6 (3), 6-3 in a match-up of 30-somethings.
Williams led 4-2 in the first set before Kerber won three straight games to go up 5-4. Williams broke the German to tie it 5-all and then held for a 6-5 lead. But Kerber held in the next game to force the tiebreaker, which she dominated.
Williams fought off two break points to tie the second set 2-all before Kerber again won three games in arrow for a 5-2 lead. She broke Williams in the match's longest game that went to deuce five times when Williams's forehand went wide.
Williams alternately smacked winners from the baseline and sprayed shots beyond the lines. The 38-year-old former world No. 1 was a semifinalist in the desert last year.
But Williams hasn't made it farther than the quarterfinals at any Premier Mandatory or Grand Slam tourney since last year's BNP Paribas Open. Until Kerber stopped her, Williams had won four matches in a row for the first time since last year in the desert.
''I played the best I could here,'' she said.
Bencic was pushed to three sets for the first time in four matches at the tournament. She was coming off a straight-set upset of defending champion and top-ranked Naomi Osaka in the fourth round.
Pliskova raced to 4-1 lead before wrapping up the second set. In the third, she overcame a break point to hold at 2-all but only won one more game the rest of the way.
''Physically, it was tough somehow, and the wind didn't help much,'' Pliskova said. ''So my serve was bad, my shots were bad.''
Bencic improved to 18-3 this year. She won her third career title at Dubai last month and her first since 2015. The 22-year-old Swiss player missed five months in 2017 after wrist surgery.
''When you're confident, you can really just trust your instincts and you don't have to think about it at all,'' Bencic said. ''I'm definitely playing how I feel it, and it's going well so I'm not planning on changing that.''