Science, Technology, Engineering, and Mathematics (STEM) education is essential for developing future-ready learners in both secondary and higher education levels. However, as students transition to higher education, many encounter challenges with independent learning and research. This can negatively impact their Higher-Order Thinking Skills (HOTS), engagement, and practical expertise. This study introduces a solution: Computational Thinking Scaffolding (CTS) in the Jupyter Notebook environment, designed to enhance STEM education at the tertiary level. CTS incorporates five phases: Decomposition, Pattern Recognition, Abstraction, Algorithm Design, and Evaluation. Utilizing a quasi-experimental method, we assessed the impact of CTS on the HOTS, engagement, and practical skills of undergraduate and postgraduate students. Our findings hold substantial relevance for university educators, academic advisors, and curriculum designers aiming to enhance students' HOTS and hands-on capabilities in STEM disciplines. The results validate the effectiveness of CTS in elevating tertiary STEM learning outcomes, and they spotlight the adaptability of the Jupyter Notebook as a valuable tool in higher education. In conclusion, our research underscores the merits of CTS for improving outcomes in higher STEM education and sets a benchmark for future endeavors in this domain.