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The world No.4, from Poland, came back from a break down in each set – as well as saving two set points in the first-set tiebreak – to level her head-to-head record with Halep at 2-2.
After taking out the WTA 1000 tournament in Doha last month, Swiatek has not had it all her way this week in California. Aside from a 6-1 6-0 trouncing of Madison Keys, the 20-year-old had to fight from a set down in her opening three matches.
After a tight first set, Halep won three games in a row to take a 4-2 lead, but it was here Swiatek started to open up on return of serve.
She was ultimately able to capitalise on Halep's second serve, winning 14 of a total 21 points when given a second look, to earn five service breaks for the match.
Swiatek is now at least guaranteed to reach a career-high world number three ranking with, and a win in the final would move her to No.2, behind only Australia's Ashleigh Barty.
She will meet Maria Sakkari in the final on Monday (AEDT), who broke down in tears after her hectic 6-2 4-6 6-1 win over Paula Badosa in the late match.
Despite Badosa having a higher first-serve rate than her opponent in the first set at 53.9 per cent, Sakkari was all over the second serve, winning nine out of a total 12 points.
After powering through the first set with flat hitting, the world No.6, from Greece, lost momentum in the second and forced play with rushed shot selection after getting broken early.
She still managed one of the shots of the match in trying to save that break of serve, scrambling across court to hit an underarm pass down the line.
Badosa kept her composure on serve to take the second set, winning 21 out of 29 points at an improved 72.9 per cent. Sakkari regrouped and exhibited her unique court coverage, however, taking the win after getting an early break.
Sakkari immediately broke down in tears afterwards, upon making her first WTA 1000 final and defeating the defending champion at Indian Wells.