During wakeful rest, individuals make small eye movements during fixation. We examined how these endogenously driven oculomotor patterns impact topography and topology of functional brain networks. We used a dataset consisting of eyes-open resting-state (RS) fMRI data with simultaneous eye tracking. The eye-tracking data indicated minor movements during rest, which correlated modestly with RS BOLD data. However, eye-tracking data correlated well with echo-planar imaging time series sampled from the area of the eye-orbit (EO-EPI), which is a signal previously used to identify eye movements during exogenous saccades and movie viewing. Further analyses showed that EO-EPI data were correlated with activity in an extensive motor and sensorimotor network, including components of the dorsal attention network and the frontal eye fields. Partialling out variance related to EO-EPI from RS data reduced connectivity, primarily between sensorimotor and visual areas. It also produced networks with higher modularity, lower mean connectivity strength, and lower mean clustering coefficient. Our results highlight new aspects of endogenous eye movement control during wakeful rest. They show that oculomotor-related contributions form an important component of RS network topology, and that those should be considered in interpreting differences in network structure between populations or as a function of different experimental conditions.