First-principles molecular dynamics simulations at constant pressure have been used to investigate the mechanisms of compression of liquid SiO2. Liquid SiO2 is found to become denser than quartz at a pressure of about 6 GPa, in agreement with extrapolations of lower pressure experimental data. The high compressibility of the liquid is traced to medium-range changes in the topology of the atomic network. These changes consist in an increase of network connectivity caused by the pressure-induced appearance of coordination defects.