This paper aims to investigate whether online private supplementary education, also known as shadow education, can alleviate educational inequality and what types of mechanisms can help alleviate it. We investigate this using an online learning platform dataset (3,603 anonymous students from China) with additional data from multiple sources and employ geospatial analyses to measure students' socioeconomic, regional and rural/urban inequalities. We find that taking part in online education narrows the performance gap in mathematics between privileged and unprivileged students in terms of school status and regional disparity in China. Theoretically, two micro-level mechanisms explain the alleviating differences: (1) equal access mechanism: students from lower city tiers and low-status schools show greater score improvement when having equal access to online education; (2) equal quality mechanism: students from rural regions improve their in-class rankings more substantially if they receive equal quality online education with the same tutoring and learning environment alongside urban students. This study comprehensively looks at the different effects of two mechanisms of online education--equal access and equal quality--for alleviating various types of inequality. Thus we speak to both educational inequality and digital inequality theory, finding that equal access to online education is not enough for rural students, as they also need access to classes of equal educational quality with their urban counterparts.