Background: Human papillomavirus (HPV) vaccination is crucial for preventing HPV-related cancers, yet vaccination rates remain suboptimal, particularly in Florida. Social influence, including family and peer support, may shape parental decisions to vaccinate their children. In this study, we examined the role of social networks (online and offline) in parental intention to vaccinate their 11- to 12-year-old children against HPV. Methods: We conducted a cross-sectional survey among 746 parents in Florida as part of the Text & Talk trial (2022–2023). Among other questions, parents reported on their intention to vaccinate, perceived social norms, and support received from up to three reported confidants. We performed logistic regression and multivariable analyses to assess the relationship between network support, social norms, and vaccination intent. Results: Seventy percent of parents intended to vaccinate their children. Greater support from the first reported confidant was significantly associated with higher vaccination intention (OR = 1.30, p < 0.0001). Perceived norms among friends (p = 0.01) and higher overall network support (p < 0.0001) were also predictive of intent. The higher the percentage of reported family members, the higher the support received for the vaccine (p = 0.04). Conclusions: Social support, particularly from close confidants and peers, plays a critical role in shaping parental HPV vaccination decisions while accounting for perceived social norms. Public health interventions can leverage peer networks alongside family support to enhance HPV vaccine uptake.