Smartphone use, particularly at night, has been shown to provoke various circadian sleep–wake rhythm disorders such as insomnia and excessive daytime tiredness. This relationship has been mainly scrutinized among patient groups with higher rates of smartphone usage, particularly adolescents and children. However, it remains obscure how smartphone usage impacts sleep parameters in adults, especially undergraduate college students. This study sought to (1) investigate the association between smartphone use (actual screen time) and four sleep parameters: Pittsburgh sleep quality score (PSQI), self-reported screen time, bedtime, and rise time; (2) compare the seven PSQI components between good and poor sleep quality subjects. In total, 264 undergraduate medical students (aged 17 to 25 years) were recruited from the Government Doon Medical College, Dehradun, India. All participants completed a sleep questionnaire, which was electronically shared via a WhatsApp invitation link. Hierarchical and multinomial regression analyses were performed in relation to (1) and (2). The average PSQI score was 5.03 ± 0.86, with approximately one in two respondents (48.3%) having a poor sleep index. Smartphone use significantly predicted respondents’ PSQI score (β = 0.142, p = 0.040, R2 = 0.027), perceived screen time (β = 0.113, p = 0.043, R2 = 343), bedtime (β = 0.106, p = 0.042, R2 = 045), and rise time (β = 0.174, p = 0.015, R2 = 0.028). When comparing poor-quality sleep (PSQI ≥ 5) to good-quality sleep (PSQI < 5), with good-quality sleep as the reference, except sleep efficiency and sleep medications (p > 0.05), five PSQI components declined significantly: subjective sleep quality (β = −0.096, p < 0.001); sleep latency (β = −0.034, p < 0.001); sleep duration (β = −0.038, p < 0.001); sleep disturbances (β = 1.234, p < 0.001); and sleep dysfunction (β = −0.077, p < 0.001). Consequently, public health policymakers should take this evidence into account when developing guidelines around smartphone use—i.e., the when, where, and how much smartphone use—to promote improved sleep behaviour and reduce the rate of sleep–wake rhythm disorders.