The objective of the research was to explain the satisfaction of students at a private university in Lima, Peru, by applying structural equations. The study aimed to explain the perceived quality of service and how it contributes to student loyalty and institutional image. A purposefully designed quantitative survey was administered to a convenience sample of third-semester university students, considering the semesters 2022-I, 2022-II, and 2023-I. A total of 655 responses were included in the analysis. Descriptive and inferential analyses were conducted to test the proposed hypotheses and identify findings. The results demonstrate a statistical relationship between the variables. The quality of service perceived by the university students almost entirely (99%) explained their satisfaction with the university services provided. Satisfaction, in turn, influences the institutional image by 91% and loyalty by 47%. The image perceived by the students accounts for 39% of their loyalty to the university they attend. Given that the development of student competencies is a primary objective of higher education, this is important because the participants are preparing for qualified employment. For this reason, the use of quality surveys in education is of interest to academics, communities, and governments alike. Although the quality results of this study are admirable, based on them, the dimensions of quality can continue to be reinforced over time. Studying service provision, student satisfaction, and loyalty can help educators and institutions improve learning.