We measure the rate of D0-D̄0 mixing with the observable yCP=(τKπ/τKK)-1, where τKK and τKπ are, respectively, the mean lifetimes of CP-even D0→K+K- and CP-mixed D0→K-π+ decays, using a data sample of 384fb-1 collected by the BABAR detector at the SLAC PEP-II asymmetric-energy B Factory. From a sample of D0 and D̄0 decays where the initial flavor of the decaying meson is not determined, we obtain yCP=[1.12±0.26(stat)±0.22(syst)]%, which excludes the no-mixing hypothesis at 3.3σ, including both statistical and systematic uncertainties. This result is in good agreement with a previous BABAR measurement of yCP obtained from a sample of D*+→D0π+ events, where the D0 decays to K-π+, K+K-, and π+π-, which is disjoint with the untagged D0 events used here. Combining the two results taking into account statistical and systematic uncertainties, where the systematic uncertainties are assumed to be 100% correlated, we find yCP=[1.16±0.22(stat)±0. 18(syst)]%, which excludes the no-mixing hypothesis at 4.1σ. © 2009 The American Physical Society.