National ranking systems of the universities in India, and the Open Access initiatives, emphasize the roles of research publications towards enhancing the national research output by achieving higher visibility for the novel works and their citations. The present study insights from the critical analyses of the institutional performances in the top NIRF-ranked universities of the last six years and Scopus-indexed publications. The impacts of constraining factors such as the COVID-19 pandemic on research publications have also been assessed by mapping the annual growth rate (AGR) for each of these universities. Results of the investigation show that the outputs of many of the universities surveyed (n=12 out of 14) had been adversely affected by the pandemic during 2020, regarding the number of publications an affiliated researcher published in SCOPUS-indexed journals. Further, the study discusses the best practices adopted by the top-ranked Indian universities publishing open access (OA) resources. The read and publish agreements with leading publishers, the visibility of the OA publications from deemed-to-be universities like MAHE, Manipal was about 44.79%. Other action plans to boost research outputs, such as providing APC charges by the universities for the OA publications (e.g. VIT, Vellore), boosted the inclination towards open-access publications. The present study illustrates case-specificity in associations between AGR and NIRF-ranking for only two universities (IISc Bangalore and MAHE Manipal) ranked within the top 10 universities. This illustrates the deeper commitment to the best practices within these universities as reasons for higher productivity despite the pandemic scenario.