As COVID-19 has become a normalized seasonal infectious disease that may break out any time, online learning has also become an important and normalized learning mode during the post-epidemic period. Promoting students' online learning engagements is the premise to ensure online learning effectiveness. Self-determination theory (SDT) can offer new insights on how to stimulate and maintain students' online learning engagements. This study aimed to explore SDT's contribution to students' online learning engagements by examining the relationship among teacher support dimensions, students' basic psychological needs, and online learning engagements. A theoretical model was established on the basis of existing research. The model was then tested with 1073 K-12 students who participated in online learning at home in western China during the COVID-19 outbreak in 2022 as sample data. Results found that (1) teacher autonomy support and involvement significantly predicted students' perceived autonomy, competence, and relatedness need satisfaction, whereas teacher structure significantly and negatively influenced students' perceptions of the three basic psychological needs satisfaction; (2) Students' perceived autonomy and competence need satisfaction significantly and positively influenced their online learning cognitive and behavioral engagements but had no significant positive influence on their online learning emotional engagement; (3) Students' perceived relatedness need satisfaction significantly and positively influenced their online learning behavioral and emotional engagements but significantly and negatively influenced their online learning cognitive engagement. On the basis of the above findings, we put forward some future research directions and implications that can help improve the understanding of SDT's contribution to students' online learning engagements.