The relevance of the study is due to the need to obtain reliable data on the components of effective teaching that affect important learning outcomes, such as motivation, engagement, academic performance, and well-being of school students. The purpose of the study was to analyze the contribution of three, actively discussed in the literature, psychological and pedagogical indicators of teaching quality, assessed by the school students, to their engagement, psychological well-being and academic performance. The study involved 2028 eighth-grade students (1085 girls, 906 boys and 35 of unspecified gender; mean age - 13.96, SD = 0.46) from 73 schools and 16 regions of the Russian Federation. The analysis of the respondents’ assessments included such indicators of teaching quality as the relevance of the learning content, psychological and instrumental support, as well as school engagement, indifference, academic performance and indicators of their satisfaction (with themselves, their teachers and school). The results of the regression analysis showed that the perceived psychological support from the teacher was the strongest predictor of the growth of all the types of educational engagement of school students and the decrease of all the types of educational indifference; besides, this component of teaching quality was a predictor of well-being in the context of school life (including the respondents’ satisfaction with their school, their teachers and themselves). The teacher’s instrumental support was the next most important predictor of cognitive and emotional engagement of the students and, no less important, was a negative predictor of all the types of learning indifference; it was also a predictor of the students’ satisfaction with their school and relationships with their teachers. Thus, the present study, conducted on a large and representative sample of Russian school students, has shown the positive effects of two components of teaching quality, namely, psychological support and instrumental support provided by the teacher. The effects of actual learning content are less clear, which casts doubt on the importance of teachers emphasizing the connection between the educational material and real life in order to maintain the motivation of school students. The results obtained can be used for training and retraining school teachers and improving teaching quality in Russian schools.