Management research explores the collaboration between humans and artificial intelligence (AI) algorithms on decision-making tasks, emphasizing the complementarity of human and AI’s heterogeneous cognitive skills. Employing a resource-based view, we challenge the notion that such within-skills complementarity explains performance improvements through human-AI collaboration on structured decision-making tasks. Instead, we propose that performance improvements arise primarily from across-skills complementarity, where AI largely substitutes humans’ cognitive skills, allowing them to leverage other skill domains, such as their unique social skills. Examining the adoption of an AI-based sales system in a leading wholesale company, we find that customer managers using AI’s cognitive skills for structured decision-making tasks refocus on applying their unique social skills for relational tasks, which is associated with a higher sales performance. Our findings challenge the prevailing emphasis on cognitive complementarity, suggesting that, in structured decision-making contexts, human contributions to human-AI collaboration arise primarily from social skills complementing AI's cognitive functions.