Measurements of K∗ (892) 0 and φ(1020)resonance production in Pb–Pb and pp collisions at √ sNN = 5.02 TeV with the ALICE detector at the Large Hadron Collider are reported. The resonances are measured at midrapidity (|y| < 0.5) via their hadronic decay channels and the transverse momentum (pT) distributions are obtained for various collision centrality classes up to pT = 20 GeV/c. The pT-integrated yield ratio K∗ (892) 0/K in Pb–Pb collisions shows significant suppression relative to pp collisions and decreases towards more central collisions. In contrast, the φ(1020)/K ratio does not show any suppression. Furthermore, the measured K∗ (892) 0/K ratio in central Pb–Pb collisions is significantly suppressed with respect to the expectations based on a thermal model calculation, while the φ(1020)/K ratio agrees with the model prediction. These measurements are an experimental demonstration of rescattering of K∗ (892) 0 decay products in the hadronic phase of the collisions. The K∗ (892) 0/K yield ratios in Pb–Pb and pp collisions are used to estimate the time duration between chemical and kinetic freeze-out, which is found to be ∼ 4–7 fm/c for central collisions. The pT-differential ratios of K∗ (892) 0/K, φ(1020)/K, K∗ (892) 0/π, φ(1020)/π, p/K ∗ (892) 0 and p/φ(1020) are also presented for Pb–Pb and pp collisions at √ sNN = 5.02 TeV. These ratios show that the rescattering effect is predominantly a low-pT phenomenon.