Although we must prioritize the processing of task-relevant information to navigate life, our ability to do so fluctuates across time. Previous work has identified fMRI functional connectivity (FC) networks that predict an individual's ability to sustain attention and vary with attentional state from 1 min to the next. However, traditional dynamic FC approaches typically lack the temporal precision to capture moment-to-moment network fluctuations. Recently, researchers have "unfurled" traditional FC matrices in "edge cofluctuation time series" which measure timepoint-by-timepoint cofluctuations between regions. Here we apply event-based and parametric fMRI analyses to edge time series to capture moment-to-moment fluctuations in networks related to attention. In two independent fMRI datasets examining young adults of both sexes in which participants performed a sustained attention task, we identified a reliable set of edges that rapidly deflects in response to rare task events. Another set of edges varies with continuous fluctuations in attention and overlaps with a previously defined set of edges associated with individual differences in sustained attention. Demonstrating that edge-based analyses are not simply redundant with traditional regions-of-interest-based approaches, up to one-third of reliably deflected edges were not predicted from univariate activity patterns alone. These results reveal the large potential in combining traditional fMRI analyses with edge time series to identify rapid reconfigurations in networks across the brain.