The purpose of this study was to evaluate a progressive functional analysis (FA) model and function-based intervention delivered by caregivers with coaching via telehealth. Children diagnosed with autism and at least one caregiver (e.g., parent) participated in the study. We conducted three assessments prior to and following intervention: a researcher-developed 10-min observation, the Parental Stress Index, and the externalizing section of the Vineland Adaptive Behavior Rating Scales, Third Edition (VABS-3). We included 47 participants in the present evaluation of the progressive FA model. We identified the function of challenging behavior for 36 participants. A function was not identified for nine participants who exhibited low or no challenging behavior during the assessment; the results were inconclusive for two participants. For the 17 participants who participated in the intervention evaluation phase, each of the participants achieved the mastery criterion, which was an 80% reduction in challenging behavior for most participants. Additionally, there was a statistically significant decrease in the VABS-3 externalizing behavior measure from pre- to post-assessment, although neither of the other pre-post measures resulted in statistically significant changes. This study replicates and extends previous research, supporting the use of progressive FA model and function-based interventions to improve challenging behavior.