We present a measurement of D0-D0bar mixing and CP violation using the ratio of lifetimes simultaneously extracted from a sample of D0 mesons produced through the flavor-tagged process D*+ -> D0 pi+, where D0 decays to K-+pi+-, K-K+, or pi-pi+, along with the untagged decays D0 -> K-+pi+- and D0 -> K-K+. The lifetimes of the CP-even, Cabibbo-suppressed modes K-K+ and pi-pi+ are compared to that of the CP-mixed mode K-+pi+- in order to measure yCP and DeltaY. We obtain yCP = [0.72 +- 0.18 (stat) +- 0.12 (syst)]% and DeltaY = [0.09 +- 0.26 (stat) +- 0.06 (syst)]%, where DeltaY constrains possible CP violation. The yCP result excludes the null mixing hypothesis at 3.3 sigma significance. This analysis is based on an integrated luminosity of 468 fb-1 collected with the BaBar detector at the PEP-II asymmetric-energy e+e- collider.