Learning engagement is a crucial factor affecting the quality of learning and holds significant value in promoting student development and enhancing teaching quality. By using time-lagged data from four schools and considering intentional self-regulation, this study integrates three types of relationships (parent-child, teacher-student, and peer relationships) into the same research framework to examine their impacts on learning engagement and the underlying mechanisms among high school students. The findings reveal that parent-child, teacher-student, and peer relationships all significantly positively affect high school students' learning engagement. Intentional self-regulation plays a partial mediation effect between parent-child relationship and learning engagement, teacher-student relationship and learning engagement, along with peer relationship and learning engagement. The unique effect of peer relationship on learning engagement is significantly greater than that of teacher-student relationship but is not significantly greater than that of parent-child relationship. To better create a supportive synergy for enhancing students' learning engagement, it is suggested that families and schools provide consistent learning support within their capabilities.