Fine-tuning on generalized tasks such as instruction following, code generation, and mathematics has been shown to enhance language models' performance on a range of tasks. Nevertheless, explanations of how such fine-tuning influences the internal computations in these models remain elusive. We study how fine-tuning affects the internal mechanisms implemented in language models. As a case study, we explore the property of entity tracking, a crucial facet of language comprehension, where models fine-tuned on mathematics have substantial performance gains. We identify a mechanism that enables entity tracking and show that (i) both the original model and its fine-tuned version implement entity tracking with the same circuit. In fact, the entity tracking circuit of the fine-tuned version performs better than the full original model. (ii) The circuits of all the models implement roughly the same functionality, that is entity tracking is performed by tracking the position of the correct entity in both the original model and its fine-tuned version. (iii) Performance boost in the fine-tuned model is primarily attributed to its improved ability to handle positional information. To uncover these findings, we employ two methods: DCM, which automatically detects model components responsible for specific semantics, and CMAP, a new approach for patching activations across models to reveal improved mechanisms. Our findings suggest that fine-tuning enhances, rather than fundamentally alters, the mechanistic operation of the model.