The fourth-seeded Spaniard on Friday afternoon did not drop her serve once and converted three of the nine break-point chances she created to take the match in just over an hour and a half, Efe news reported.
With the win, the 22-year-old Muguruza ran her career mark against the 41st-ranked Babos to 4-0.
In Saturday's first semi-final, Muguruza will take on Czech No.15 seed Karolina Pliskova, a 6-3, 4-6, 6-2 winner Friday over seventh-seeded Russian Svetlana Kuznetsova.
Second-seeded German Angelique Kerber also advanced to the semi-finals on Friday with a 4-6, 6-3, 6-0 win over Spain's Carla Suarez Navarro and is now just two wins from wresting the No.1 ranking away from American legend Serena Williams, who withdrew from the Western & Southern Open due to a shoulder injury.
The second-seeded Kerber will square off against either Polish No.5 seed Agnieszka Radwanska or third-seeded Romanian Simona Halep in Saturday's second semifinal.
In the men's event in Cincinnati, fourth-seeded Canadian Milos Raonic cruised to a 6-3, 6-4 victory over eighth-seeded Austrian Dominic Thiem and will next play either Scottish top seed Andy Murray or Australia's Bernard Tomic in Saturday evening's first semifinal.
The second semi-final will pit Bulgaria's Grigor Dimitrov, a 7-6 (10-8), 6-2 winner over American Steve Johnson, against Croatian No.12 seed Marin Cilic, who defeated countryman Borna Coric 6-2, 0-0, ret.
The Western & Southern Open is one of the biggest hard-court tournaments on the ATP Tour and WTA Tour calendars and a key tune-up event for the US Open, which gets under way on August 29.
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