Abstract Background: Rational use of medicine in a teaching hospital is critical for effective and efficient patient care. This study assessed prescription, dispensing, and rational medicine in a Nigerian tertiary care facility. Materials and Method: This was an analytic cross-sectional study with data collected using validated tools underpinned by the World Health Organisation (WHO) and the International Network for the Rational Use of Drugs (INRUD) core indicators for prescription, patient care, and facility. A cluster sample of 10 specialist clinics and servicing pharmacies were selected. Simple random sampling was deployed to retrieve 600 medicine prescriptions in the pharmacies over a six-month period (June 1, 2021–November 30, 2021). Patient care indicators were assessed using 330 patient encounters, and 48 prescribers across the 10 clinics were randomly selected for assessing factors influencing prescribing practices. Exploratory and confirmatory analyses were conducted with SPSS version 25, and findings were compared with WHO/INRUD recommendations. Results: The mean medicine count per visit was 3.4 ± 1.9 with 40.2% and 24.8% of prescriptions containing antibiotics and injections, respectively. Nonproprietary prescriptions were 43.6% and 97.1% of medicines prescribed were contained the essential medicines list (EML). The mean times spent were 17.5 ± 8.0 and 7.7 ± 3.8 min with prescribers and dispensers, respectively. Most (99.8%) of the dispensed medicines were labeled properly while 82% of patients knew the regimen. Most (93.3%) tracer medicines were in the pharmacies, but no clinic had copies of the EML. Significant differences in prescription and patient care indicators were reported across specialty units. Conclusion: Gaps exist in medicine prescription and dispensing. The preponderance of brand prescription, polypharmacy, and antibiotic prescription calls for implementation of extant policies and guidelines on the use of medicines as well as training and monitoring on rational medicine use among prescribers and dispensers in the teaching hospital.