Connecting with peers through social networking sites (SNS) is an intrinsic part of adolescents’ current lives. However, when SNS are used to satisfy distorted psychological needs, problematic social media use (PSMU) may emerge as a negative consequence. The Interaction Person-Affect-Cognition-Execution (I-PACE) model provides theoretical grounds for exploring different pathways that may lead to PSMU. The present study aimed at contributing to this expanding scientific literature by testing a model that considers low emotional intelligence (EI) as a vulnerability factor, stress and maladaptive coping strategies as responses to conflicting situations, and PSMU as a possible negative consequence that adolescents who have difficulties managing stressful situations may present. The sample consisted of 2068 Spanish adolescents (46.2% male, 53.8% female), within the ages of 12 and 19 (M = 14.61, SD = 1.62), who completed self-report measures of the previously mentioned constructs. Model 6 of the PROCESS macro for SPSS was used to test a serial mediation model where EI was the independent variable, stress was the first mediator, maladaptive coping strategies were the second mediator, and PSMU was the outcome variable. Age and sex were entered as covariates. The results indicate that the multiple mediation model accounted for 14.5% of the variance in PSMU (p < 0.001), and that all direct and indirect effects were statistically significant. Our results support that stress and maladaptive coping are underlying mechanisms linking lower EI to PSMU, thus, provide promising ground to better understand and prevent poor social media use among adolescents.