Global expenditure on research and development has been increasing steadily over the last few decades. Several studies in developed countries have shown that increased research funding to individual researchers leads to increased research output, while having mixed effects on research quality. However, very few studies have analyzed the relationship between research funding and research productivity (comprising research output and quality) in the context of developing countries. In this paper, I examine the relationship between government research funding and research productivity at science and technology (S&T) universities in India. I find a positive relationship between government research funding and research output, however the relationship between government research funding and research quality is surprisingly negative. My results imply that Indian policymakers should substantially increase the research funding for Indian institutions to compete with their international peers in terms of research output. However, improving research quality might require supplementary measures such as attracting world-class faculty members and nurturing the next generation of researchers at Indian universities.