Patterns of functional interactions across distributed brain regions are suggested to provide a scaffold for the conscious processing of information, with marked topological alterations observed in loss of consciousness. However, establishing a firm link between macro-scale brain network organisation and conscious cognition requires direct investigations into neuropsychologically-relevant architectural modifications across systematic reductions in consciousness. Here we assessed both global and regional disturbances to brain graphs in a group of healthy participants across baseline resting state fMRI as well as two distinct levels of propofol-induced sedation. We found a persistent modular architecture, yet significant reorganisation of brain hubs that formed parts of a wider rich-club collective. Furthermore, the reduction in the strength of rich-club connectivity was significantly associated with the participants' performance in a semantic judgment task, indicating the importance of this higher-order topological feature for conscious cognition. These results highlight a remarkable interplay between global and regional properties of brain functional interactions in supporting conscious cognition that is relevant to our understanding of clinical disorders of consciousness.