Feature-based attentional selection is accomplished by increasing the gain of sensory neurons encoding target-relevant features while decreasing that of other features. But how do these mechanisms work when targets and distractors share features? We investigated this in a simplified color-shape conjunction search task using ERP components (N2pc, PD, and SPCN) that index lateralized attentional processing. In Experiment 1, we manipulated the presence and frequency of color distractors while holding shape distractors constant. We tested the hypothesis that the color distractor would capture attention, requiring active suppression such that processing of the target can continue. Consistent with this hypothesis, we found that color distractors consistently captured attention, as indexed by a significant N2pc, but were reactively suppressed (indexed by PD). Interestingly, when the color distractor was present, target processing was sustained (indexed by SPCN), suggesting that the dynamics of attentional competition involved distractor suppression interlinked with sustained target processing. In Experiment 2, we examined the contribution of shape to the dynamics of attentional competition under similar conditions. In contrast to color distractors, shape distractors did not reliably capture attention, even when the color distractor was very frequent and attending to target shape would be beneficial. Together, these results suggest that target-colored objects are prioritized during color-shape conjunction search, and the ability to select the target is delayed while target-colored distractors are actively suppressed.