Stephens pleased the partisan Yale University crowd with a 6-4, 6-4 triumph over Slovakian qualifier Anna Schmiedlova.
Third-seeded Wozniacki, however, had to wait out 2-hour rain delay before her match with China's Peng Shuai. The Dane dropped with the first set 2-6 but was leading 3-1 in the second when Peng retired due to dizziness.
Three-time 2013 titlist Simona Halep extended her surge Monday, dispatching Slovak Daniela Hantuchova 6-2, 6-1, while Russians Elena Vesnina, Ekaterina Makarova and Anastasia Pavlyuchenkova, and German wild card Julia Goerges also advanced.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged