High levels of perceived stress and anxiety among university students are a global concern and are known to negatively influence sleep. However, few studies have explored how stress response styles, like psychological resilience and rumination, might alter these relationships. Using validated tools, perceived stress, anxiety, stress response styles, and sleep behaviors of undergraduate and graduate students from seven countries during the height of the COVID-19 pandemic were characterized in order to examine the relationships between these factors using mediation and moderation analyses. Students enrolled in universities in China, Ireland, Malaysia, Taiwan, South Korea, the Netherlands, and the United States were recruited in May 2020. A total of 2254 students completed this cross-sectional study. Perceived stress and anxiety were negatively associated with sleep quality through the mediation of rumination. Increased psychological resilience weakened the relationships between perceived stress and anxiety on sleep quality. The majority of students reported that COVID-19 negatively influenced their mental health and sleep quality but not sleep duration. Based on these results, university students would likely benefit from sleep education and mental health promotion programs that include trainings to increase psychological resilience and reduce rumination, particularly during times of increased stress.