This paper first screens the indicators by examining the current state of information literacy and critical thinking. The sparse principal component analysis (SPCA) algorithm and factor analysis model are combined to deeply mine the influencing factors of information literacy and critical thinking and provide an optimization path for the linkage cultivation model of information literacy and critical thinking. Finally, we validate and analyze the enhanced critical thinking abilities. The results show that the first four eigenroot coefficients of the correlation coefficient matrices of the proposed four main factor variables are 4.31, 3.4, 3.07, and 2.74, respectively. The eigenroots’ explanatory degrees are 33.2%, 25.7%, 21.9%, and 15.1%, respectively. The four extracted principal factors can explain 95.85% of the information in the original index. The four critical indicators of questioning, discriminating, comparing, and controlling are significantly positively correlated between the two. The synthesis of the usefulness of the four critical indicators revealed that 97.5% agreed that they could improve students’ information literacy and critical thinking skills. This study positively supports and promotes the improvement of students’ information literacy and critical thinking skills in the educational information technology environment.