'Kick and kill' cure strategies aim to induce HIV protein expression in latently infected cells (kick), and thus trigger their elimination by cytolytic T cells (kill). In the Research in Viral Eradication of HIV Reservoirs trial (NCT02336074), people diagnosed with primary HIV infection received immediate antiretroviral therapy (ART) and were randomised 24 weeks later to either a latency-reversing agent, vorinostat, together with ChAdV63.HIVconsv and MVA.HIVconsv vaccines, or ART alone. This intervention conferred no reduction in HIV-1 reservoir size over ART alone, despite boosting virus-specific CD4+ and CD8+ T cells. The effects of the intervention were examined at the cellular level in the two trial arms using unbiased computational analysis of polyfunctional scores. This showed that the frequency and polyfunctionality of virus-specific CD4+ and CD8+ T cell populations were significantly increased over 12 weeks post-vaccination, compared to the ART-only arm. HIV-specific IL-2-secreting CD8+ T cells also expanded significantly in the intervention arm and were correlated with antiviral activity against heterologous HIV in vitro. Therapeutic vaccination during ART commenced in primary infection can induce functional T cell responses that are phenotypically similar to those of HIV controllers. Analytical therapy interruption may help determine their ability to control HIV in vivo.