Experiments show activation of the left dorsolateral prefrontal cortex (DLPFC) in motor imagery (MI) tasks, but its functional role requires further investigation. Here, we address this issue by applying repetitive transcranial magnetic stimulation (rTMS) to the left DLPFC and evaluating its effect on brain activity and the latency of MI response. This is a randomized, sham-controlled EEG study. Participants were randomly assigned to receive sham (15 subjects) or real high-frequency rTMS (15 subjects). We performed EEG sensor-level, source-level, and connectivity analyses to evaluate the rTMS effects. We revealed that excitatory stimulation of the left DLPFC increases theta-band power in the right precuneus (PrecuneusR) via the functional connectivity between them. The precuneus theta-band power negatively correlates with the latency of the MI response, so the rTMS speeds up the responses in 50% of participants. We suppose that posterior theta-band power reflects attention modulation of sensory processing; therefore, high power may indicate attentive processing and cause faster responses.