Spain's Garbine Muguruza powered her way into the quarter-finals of the Porsche Tennis Grand Prix in Stuttgart on Wednesday.
The 22-year-old was a bit shaky on serve in the first set and was broken twice, but she made up for that by being absolutely relentless while receiving, breaking Babos' serve four times in a row to go one set up.
Muguruza continued to pile on the pressure in the second set, claiming two more early breaks for a 3-0 lead, and Babos had to fight tooth and nail to hold her service games from that point on, saving six break points.
Despite her tenacity, there was little Babos could do to prevent Muguruza from completing a 6-2, 6-2 victory in 77 minutes.
Second seed Angelique Kerber was also in action, taking on fellow German Annika Beck, recovering from a slow start to secure a 4-6, 6-3, 6-1 victory.
Other local players to advance on the day included Julia Georges and Andrea Petkovic. Georges beat Alize Cornet 6-4, 6-0 while Petkovic defeated Kristina Mladenovic 6-2, 6-4.
Sixth seed Roberta Vinci of Italy was given a real test by Russian Ekaterina Makarova, but eventually prevailed 7-6 (7-3), 4-6, 6-4.
An all Czech battle between Karolina Pliskova and Lucie Safarova went to the former after a two-and-half-four battle, with Pliskova winning 7-6 (7-4), 4-6, 7-5.