Open-book examinations (OBEs) will likely become increasingly important assessment tools. We investigated how access to open-book resources affected questions testing factual recall, which might be easy to look-up, versus questions testing higher-order cognitive domains. Few studies have investigated OBEs using modern Internet resources or as summative assessments. We compared performance on an examination conducted as a traditional closed-book exam (CBE) in 2019 (N = 320) and a remote OBE with free access to Internet resources in 2020 (N = 337) due to COVID-19. This summative, end-of-year assessment focused on basic science for second-year medical students. We categorized questions by Bloom's taxonomy ('Remember', versus 'Understand/Apply'). We predicted higher performance on the OBE, driven by higher performance on 'Remember' questions. We used an item-centric analysis by using performance per item over all examinees as the outcome variable in logistic regression, with terms 'Open-Book, 'Bloom Category' and their interaction. Performance was higher on OBE questions than CBE questions (OR 2.2, 95% CI: 2.14-2.39), and higher on 'Remember' than 'Understand/Apply' questions (OR 1.13, 95% CI: 1.09-1.19). The difference in performance between 'Remember' and 'Understand/Apply' questions was greater in the OBE than the CBE ('Open-Book' * 'Bloom Category' interaction: OR 1.2, 95% CI: 1.19-1.37). Access to open-book resources had a greater effect on performance on factual recall questions than higher-order questions, though performance was higher in the OBE overall. OBE design must consider how searching for information affects performance, particularly on questions measuring different domains of knowledge.