Acceptance of fake news is probably modulated by an intricate interplay of social, cultural, and political factors. In this study, we investigated whether individual-level cognitive factors related to thinking and decision making could influence the tendency to accept fake news. A group of volunteers responded to a COVID-19-related fake news discrimination scale as well as to questionnaires assessing their thinking style (reflective vs. intuitive) and thinking disposition (actively open-mindedness). Furthermore, they completed a computerized contingency learning task aimed at measuring their tendency to develop a causal illusion, a cognitive bias leading to perceive causal connections between non-contingent events. More actively open-minded and more reflective individuals presented higher fake news discrimination scores. In addition, those who developed weaker causal illusions in the contingency learning task were also more accurate at differentiating between fake and legitimate news. Actively open-minded thinking was the main contributor in a regression model predicting fake news discrimination.