Recently, machine learning (ML) has evolved and finds its application in higher education (HE) for various data analysis. Studies have shown that such an emerging field in educational technology provides meaningful insights into several dimensions of educational quality. An in-depth analysis of the application of ML could have a positive impact on the HE sector. However, there is a scarcity of a systematic review of HE literature to gain from the overarching trends and patterns discovered using ML. This paper conducts a systematic review and meta-analyses of research studies that have reported on the application of ML in HE. The differentiating factors of this study are primarily vested in the meta-analyses including a specific focus on student academic performance, at-risk, and attrition in HE. Our detailed investigation adopts an evidence-based framework called PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) for reporting the findings of our systematic review and meta-analyses of literature on the use of ML models, algorithms, evaluation metrics, and other criteria, including demographics for assessing student academic performance, at-risk and attrition in HE. After undergoing the PRISMA steps such as selection criteria and filtering, we arrive at a small-scale dataset of 89 relevant studies published from 2010 to 2020 for an in-depth analysis. The results show the outcomes of the quantitative analysis of the application of ML types, models, evaluation metrics, and other related demographics and provide quality insights of publication patterns and future trends towards predicting and monitoring student academic progress in HE.