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Both players tussled to take an early lead in the first game with two break points being squandered, before Bencic eventually prevailed to move ahead of her Romanian opponent in the opening set.
Halep was able to find the first break of serve in the fifth game, however, to get a foothold on the set, which she eventually took 6-4.
The world number three found the second set easier going, grabbing three breaks of serve to win 6-1 and take the match in the process.
Halep will now face Zarina Diyas in the next round.