As open publication has become a goal in scholarly communication, interest in how it relates to other features of the research process has grown. This paper focuses on the relationship between funding and open access (OA) in the Spanish National Research Council’s Web of Science publications in three scientific fields with different research practices, namely, Biology & Biomedicine (BIOL), Humanities & Social Sciences (HSS) and Materials Science (MATE). Firstly, the three fields are characterised in relation to OA practices (OA status and OA routes) and acknowledged funding (funding status and funding origin). Secondly, the relationship between OA and funding is explored, and the role of additional influential factors, such as the internationality of research and national/foreign leadership of papers, is unravelled through logistic regression. BIOL shows a higher OA share (66%) than do the other two fields (around 33%). Funded research shows higher OA rates than unfunded research in the experimental fields, but not in HSS, where it is related to a shift towards more publications with article-processing charges. The internationality of research, measured through international collaboration or foreign funding, increases OA, albeit with differences across fields. Foreign-funded papers are more likely to be led by foreign researchers in all three fields, but a foreign first author increases the chances of OA publication in HSS only, perhaps because Spanish leaders in this field have not internalised the importance of OA. The research’s policy implications are reviewed.