Memory CD8+ T lymphocytes (CTLs) specific for antigenic peptides derived from internal viral proteins confer broad protection against distinct strains of influenza A virus (IAV). However, immune efficacy can be undermined by the emergence of escape mutants. To determine how T-cell receptor (TCR) composition relates to IAV epitope variability, we used ex vivo peptide–HLA tetramer enrichment and single-cell multiplex analysis to compare TCRs targeted to the largely conserved HLA-A0201-M158 and the hypervariable HLA-B3501-NP418 antigens. The TCRαβs for HLA-B3501-NP418+ CTLs varied among individuals and across IAV strains, indicating that a range of mutated peptides will prime different NP418-specific CTL sets. Conversely, a dominant public TRAV27/TRBV19+ TCRαβ was selected in HLA-A0201+ donors responding to M158. This public TCR cross-recognized naturally occurring M158 variants complexed with HLA-A0201. Ternary structures showed that induced-fit molecular mimicry underpins TRAV27/TRBV19+ TCR specificity for the WT and mutant M158 peptides, suggesting the possibility of universal CTL immunity in HLA-A0201+ individuals. Combined with the high population frequency of HLA-A*0201, these data potentially explain the relative conservation of M158. Moreover, our results suggest that vaccination strategies aimed at generating broad protection should incorporate variant peptides to elicit cross-reactive responses against other specificities, especially those that may be relatively infrequent among IAV-primed memory CTLs.