World number 42 Teichmann raced to a memorable victory against the three-time grand slam winner in just over an hour as the left-hand collected her sixth win against a top-20 player this season.
Half of those wins have come this year as well, with the Swiss beating Naomi Osaka, Belinda Bencic and Karolina Pliskova in a breakthrough Cincinnati campaign.
Fifth seed Anastasia Pavlyuchenkova cruised through after negotiating a difficult first set against Ana Konjuh to win 7-6 (7-3) 6-1 in just over an hour-and-a-half.
Tereza Martincova's victory over fellow Czech Katerina Siniakova did not come as easily, though, with the former edging to a 5-7 6-4 7-6 (9-7) win in more than a three-hour slog.
Martincova, who is ranked 61st in the world, miraculously recovered from 5-0 down in the tie-break to save a match point before securing her first main-draw win in Croatia.
Yulia Putintseva experienced similar difficulties against Shuai Zhang, as she also battled out in a three-hour marathon and saved a match point to eventually succeed 5-7 7-6 (9-7) 6-4.