The German took advantage of a far more consistent service game against an opponent whose serve all but deserted her.
The Taipei woman is 25th in the rankings but her game disintegrated in the second set as she won just 35% of points on her first serve and the match was over in an hour.
Beck will now play sixth seed Shuai Peng who served four aces on her way to a 6-1 6-1 victory over Japan's Ayumi Morita.
Morita forced 10 break points but could take advantage of only four and the Chinese woman took just 52 minutes to ease to victory.
Top seed Li Na had a tough first set against unseeded Mandy Minella but eventually prevailed 6-4 6-0.
There was little to choose between the pair in the first set but the Chinese player, ranked seventh in the world, dominated on her serve in the second with her Dutch opponent having no answer.
Fifth seeded Klara Zakopalova had to battle for an hour and 25 minutes against Elina Svitolina, who at 131 is ranked 103 places below her Czech opponent.
However, Zakopalova prevailed 6-4 6-3 in a scrappy match.
There was though a surprise when seventh seed Laura Robson was knocked out by Monica Niculescu 6-2 6-3.
The world number 53 was barely in the match against the Romanian but there were no such problems for eighth seed Bojana Jovanovski who beast Ying-Ying Duan 6-3 6-1.
Yi-Miao Zhou beat qualifier Jessica Pegula 6-4 6-2.