(1) The main goal of this research was to assess the effectiveness of the computer-supported collaborative learning for language learning purposes using the indicators of students’ learning outcomes and the level of their engagement, as well as to determine the most effective benchmarks for teams’ forming. (2) Methods: A total of 81 undergraduate students studying at the Humanity Institute of Peter the Great Polytechnic University voluntarily participated in the study. For our research, we used the results on final English testing and survey results on students’ engagement. Each year, three groups of students were formed into teams according to three criteria: leadership skills, academic performance and personal choices. Microsoft Excel 2016 tools were used for data interpretation: testing samples for normality, a one-way analysis of variance (ANOVA) and comparison of means. Neural network dependencies of test results were built by means of Mathematica Wolfram Software. (3) Results: According to the results of this study, the underlying principles of forming teams highly influenced the indicators of students’ English proficiency; in particular, the experiment proved the effectiveness of selecting students according to their academic performance. In addition, the correlation analysis revealed that the engagement of students played an important role and influenced the results of their learning. This was especially seen in a group where teams were distributed due to the differences in academic performance. (4) Conclusions: As the COVID-19 pandemic is an ever-changing situation, it is important to implement effective learning models that promote higher learning outcomes and students’ engagement. This study contributes to such knowledge and provides insightful implications to academia.