(1) Background: The objective of this study was to evaluate the associations of sleep quality, anxiety, and depression with cognitive performance, executive functions, and verbal fluency among women aged ≥ 65 years; (2) Methods: A cross-sectional study was conducted on 241 women (72.52 ± 3.93 years). Cognitive performance (Mini-Mental State Examination) and impairment (Montreal Cognitive Assessment), verbal fluency (Isaacs test) and executive function (Trail Making Test), Sleep quality (Pittsburgh Sleep quality Index) and anxiety and depression (Hospital Anxiety and Depression Scale) were determined; (3) Results: The linear regression analysis indicated that anxiety, depression and age, were related to lower Mini-Mental State Examination score (adjusted R2 = 0.306), and age, anxiety and daytime dysfunction were linked to reduced Montreal Cognitive Assessment score (adjusted R2 = 0.248). Age and daytime dysfunction were associated with worse verbal fluency (adjusted R2 = 0.094). Finally, sleep latency, sleep disturbances, the Pittsburgh Sleep quality Index total score were associated with longer times in TMT-A (adjusted R2 = 0.758) and TMT-B (adjusted R2 = 0.508); (4) Conclusions: Sleep quality was associated with cognitive performance, verbal fluency and executive functions. Besides, both anxiety and depression were related with cognitive performance, while only anxiety was linked to executive functions. As for confounders, age was associated with cognitive performance and verbal fluency.