BNT162b2-vaccinated individuals after Omicron BA.1 breakthrough infection have strong serum-neutralizing activity against Omicron BA.1, BA.2, and previous SARS-CoV-2 variants of concern (VOCs) yet less against the highly contagious Omicron sublineages BA.4 and BA.5 that have displaced previous variants. Because the latter sublineages are derived from Omicron BA.2, we characterized serum-neutralizing activity of COVID-19 mRNA vaccine triple-immunized individuals who experienced BA.2 breakthrough infection. We demonstrate that sera of these individuals have broadly neutralizing activity against previous VOCs and all tested Omicron sublineages, including BA.2-derived variants BA.2.12.1 and BA.4/BA.5. Furthermore, applying antibody depletion, we showed that neutralization of BA.2 and BA.4/BA.5 sublineages by BA.2 convalescent sera is driven to a considerable extent by antibodies targeting the N-terminal domain (NTD) of the spike glycoprotein. However, neutralization by Omicron BA.1 convalescent sera depends exclusively on antibodies targeting the receptor binding domain (RBD). These findings suggest that exposure to Omicron BA.2, in contrast to BA.1 spike glycoprotein, triggers substantial NTD-specific recall responses in vaccinated individuals and thereby enhances the neutralization of BA.4/BA.5 sublineages. Given the current epidemiology with a predominance of BA.2-derived sublineages such as BA.4/BA.5 and rapidly ongoing evolution, these findings helped to inform development of our Omicron BA.4/BA.5-adapted vaccine.