COVID-19 has caused the overnight migration of learning and teaching to online platforms and has significantly impacted students' learning opportunities and experiences worldwide. The results of emergency online learning have heavily relied on students' abilities to exercise agency in maintaining active motivation and engagement with online learning. Despite the wide application of motivation theories to diverse contexts, how to adapt motivation theories to develop online learning effectively and sustainably in complex and situational online learning environments is still under-investigated. Using a large sample of 14,935 postgraduate students from 31 universities in China, this study examined the effects of student motivation and engagement on students' academic achievement in the COVID-induced online learning anchored by the theoretical perspective of self-determination theory. This study made contribution to the self-determination theory by extending it to the complex emergency situation and supported its main argument that online emergency learning environments satisfying students' psychological needs of autonomy and competence promote optimal motivation, positive engagement and academic achievement. This study also contributed to reveal the 'sophisticated' nature of relatedness satisfaction in the case wherein its specific effects depend on the cultural configuration of the contexts and on the specific types of engagement. Given the fact that COVID-19 continues to be a public challenge throughout the world, implications for improving the quality of online teaching in the future were also discussed.