Breakthrough infections in SARS-CoV-2 vaccinated individuals are an ideal circumstance for the simultaneous exploration of both the vaccine-induced memory reaction to the spike (S) protein and the primary response to the membrane (M) and nucleocapsid (N) proteins generated by natural infection. We monitored 15 healthcare workers who had been vaccinated with two doses of Pfizer BioNTech BNT162b2 and were then later infected with the SARS-CoV-2 B.1.617.2. (Delta) variant, analysing the antiviral humoral and cellular immune responses. Natural infection determined an immediate and sharp rise in anti-RBD antibody titres and in the frequency of both S-specific antibody secreting cells (ASCs) and memory B lymphocytes. T cells responded promptly to infection by activating and expanding already at 2–5 days. S-specific memory and emerging M- and N-specific T cells both expressed high levels of activation markers and showed effector capacity with similar kinetics but with different magnitude. The results show that natural infection with SARS-CoV-2 in vaccinated individuals induces fully functional and rapidly expanding T and B lymphocytes in concert with the emergence of novel virus-specific T cells. This swift and punctual response also covers viral variants and captures a paradigmatic case of a healthy adaptive immune reaction to infection with a mutating virus.