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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.