In recent years control theory has been applied to biological systems with the aim of identifying the minimum set of molecular interactions that can drive the network to a required state. However, in an intra-cellular network it is unclear how control can be achieved in practice. To address this limitation we use viral infection, specifically human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV), as a paradigm to model control of an infected cell. Using a large human signalling network comprised of over 6000 human proteins and more than 34000 directed interactions, we compared two states: normal/uninfected and infected. Our network controllability analysis demonstrates how a virus efficiently brings the dynamically organised host system into its control by mostly targeting existing critical control nodes, requiring fewer nodes than in the uninfected network. The lower number of control nodes is presumably to optimise exploitation of specific sub-systems needed for virus replication and/or involved in the host response to infection. Viral infection of the human system also permits discrimination between available network-control models, which demonstrates that the minimum dominating set (MDS) method better accounts for how the biological information and signals are organised during infection by identifying most viral proteins as critical driver nodes compared to the maximum matching (MM) method. Furthermore, the host driver nodes identified by MDS are distributed throughout the pathways enabling effective control of the cell via the high 'control centrality' of the viral and targeted host nodes. Our results demonstrate that control theory gives a more complete and dynamic understanding of virus exploitation of the host system when compared with previous analyses limited to static single-state networks.