The extant literature on the integration of mobile instant messaging (MIM) into language pedagogy has documented its potential to leverage engagement and learning outcomes. Nevertheless, how individual differences in regard to emotional, sociocognitive, and motivational bearings contribute to language learning gains is hardly documented. This study is devoted to addressing this lacuna through an analysis of structural equation modeling (SEM) which explores the association between trait-emotional intelligence (TEI), online learning engagement (OLE), EFL learning motivation, and their grades in English for Academic Purposes (EAP) programs. Three-hundred-seventy-one freshmen in an Indonesian university were involved in EAP programs framed in team-based mobile language learning (TBML), mediated by Telegram as a complementary learning app. The students responded to an online survey eliciting their post-lesson perception of the abovementioned variables. Students’ course grades complemented the data collection. The results of our SEM analysis acknowledged the linear correlation from TEI, OLE, to EFL motivation as the drives to students’ learning achievement. This has also been supported by a robust correlation between the variables. The findings of the present study implicate the pedagogical potentials of TBML to scaffold self-regulated learning and satisfactory language learning gains, provided that students’ emotional intelligence, engagement, and motivation are intensively potentiated across different learning phases. Research limitations and recommendations are also explored.