Halep, playing her second match of the day, having earlier dismissed Ashleigh Barty 7-5 6-4 in their rain-delayed third-round clash, fought back from 4-1 down in the first set to rattle off 11 of the last 12 games, ousting Tsurenko 6-4 6-1.
The Rogers Cup winner will now face Aryna Sabalenka, who – after seeing off top 10 players Karolina Pliskova and Caroline Garcia earlier in the week – claimed another big win by overcoming number 13 seed Madison Keys.
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The Belarusian stunned Keys in straight sets 6-3 6-4 after Keys failed to take advantage of 10 break points and Sabalenka produced 19 winners in the one-hour, 17-minute match.
Kiki Bertens, meanwhile, beat number five seed Elina Svitolina 6-4 6-3 to reach the semi-finals.
Bertens’s shaky start saw her taken to 3-1 by Svitolina in the first set, but from there the 26-year-old took control to level the match at 4-4 and eventually served out the set.
She kept up the momentum in the second set, breaking her opponent three times and securing the win with a flawless backhand drop volley in just under 90 minutes.
Bertens will now face number eight seed Petra Kvitova, who progressed to her second semi-final Cincinnati after dismissing Elise Mertens 7-5 5-7 6-3.
Svitolina - Halep - US Open Highlights
Svitolina downs Halep to reach US Open quarter-finals