With the rapid advancement of generative artificial intelligence (GenAI), teaching and learning in higher education are undergoing profound transformations. As a foundational competency for students in the digital age, pathways to foster online mathematics learning power require exploration. Although teacher support is recognized as a critical factor, the mechanisms through which it might foster students' new digital competencies, thereby contributing to online mathematics learning power within the context of intelligent technologies remain underexplored. This study aims to construct a multiple mediation model to examine how perceived teacher support predicts online mathematics learning power through two pathways: AI literacy (the ability to leverage artificial intelligence for mathematical cognition) and the use of cognitive tools (e.g., MATLAB, GeoGebra). A questionnaire survey was conducted among 758 undergraduates enrolled in online mathematics courses at a comprehensive university in eastern China. The instruments included scales for perceived teacher support, AI literacy, cognitive tools, and online mathematics learning power. Data were analyzed using structural equation modeling and bootstrap sampling to examine direct and mediating effects. The results confirm that within the generative artificial intelligence context, perceived teacher support directly predicts students' online mathematics learning power while also indirectly predicts it by fostering AI literacy and cognitive tools proficiency. This reveals the mechanisms linking environmental support, digital competencies, and learning outcomes. This study suggests that educators adopt a teaching strategy integrating direct support, AI literacy cultivation, and cognitive tool guidance. This entails incorporating AI literacy and cognitive tools training into online mathematics course design within supportive learning environments. Doing so can effectively develop student competencies and prepare them for the intelligent era.