This study employed piecewise growth curve modeling to examine how children's executive function (EF) skills relate to different components of children's physiological response trajectory – initial arousal, reactivity, and recovery. The sample included 102 ethnically diverse kindergarteners, whose EF skills were measured using standard tasks and observer ratings. Physiological response was measured via changes in respiratory sinus arrhythmia (RSA) in response to a laboratory socio‐cognitive challenge. Children's cool and hot EF skills were differentially related to both linear and quadratic components of RSA response during the challenge. Greater hot EF skills and assessor report of EF skills during laboratory visit were related to quicker RSA recovery after the challenge. These findings demonstrate that children's physiological response is a dynamic process that encompasses physiological recovery and relates to children's self‐regulation abilities. Children's physiological response is a dynamic process that includes distinct reactivity and recovery trajectories. Discrepancies in how cool and hot EF skills relate to RSA response to the challenge task may index different utilization of these skills during social and cognitive task demands. Higher executive function skills in emotionally demanding situations were uniquely related to physiological recovery, as indexed by faster RSA augmentation following the challenge. Findings are consistent with the polyvagal perspective of social engagement and highlight the importance of studying the interplay between physiological and behavioral regulation.