Where we look is determined both by our current intentions and by the tendency of visually salient items to "catch our eye." After damage to parietal cortex, the normal process of directing attention is often profoundly impaired. Here, we tracked parietal patients' eye movements during visual search to separately map impairments in goal-directed orienting to targets versus stimulus-driven gaze shifts to salient but task-irrelevant probes. Deficits in these two distinct types of attentional selection are shown to be identical in both magnitude and spatial distribution, consistent with damage to a "priority map" that integrates goal- and stimulus-related signals to select visual targets. When goal-relevant and visually salient items compete for attention, the outcome depends on a biased competition in which the priority of contralesional targets is undervalued. On the basis of these findings, we further demonstrate that parietal patients' spatial bias (neglect) in goal-directed visual exploration can be corrected and even reversed by systematically manipulating the spatial distribution of stimulus salience in the visual array.