In the last two decades, Kenya has witnessed an exponential growth of students’ enrolment in its public universities and an oscillatory government funding in these institutions precipitating quality concerns by employers on the skills of the graduates to meet industry needs. In education finance, the sources of funds and the size of the resources are key determinants of quality education. The objective of the study was to determine the relationship between various funding sources and access to quality education in Kenya public universities using a case approach. The data collection instruments used were an interview guide, a focus group discussion guide, a student’s survey questionnaire and secondary document analysis. Data was collected from October to December 2014 in the case university from a sample population of 10 top university management staff, 36 heads of department (HoDs) and 400 undergraduate students. The study employed the education production function as a basic model of the study. The validity of the data collection instruments was established through scrutiny by thesis supervisors and the reliability test of the students’ questionnaire returned a Cronbach alpha of 0.88. F-test and analysis of variance (ANOVA) methods were used with aid of the statistical package for social science (SPSS) version 2.0. The conclusion of the study was that, the sources of funds had a positive effect on quality though the results were not significant, while government capitation, tuition and other sources of funds were significantly important for the access of quality of education in the institution (P =0.30, P = 0.018, P = 0.000). The study recommended the adoption of performance based funding to enhance quality in higher education.