We measure the time dependence of the ratio of decay rates for D0→K(+)π(-) to the Cabibbo-favored decay D(0)→K(-)π(+). The charge conjugate decays are included. A signal of 3.3×10(4) D(*+)→π(+)D(0), D(0)→K(+)π(-) decays is obtained with D0 proper decay times between 0.75 and 10 mean D0 lifetimes. The data were recorded with the CDF II detector at the Fermilab Tevatron and correspond to an integrated luminosity of 9.6 fb(-1) for pp¯ collisions at √s=1.96 TeV. Assuming CP conservation, we search for D0-D¯0 mixing and measure the mixing parameters to be R(D)=(3.51±0.35)×10(-3), y'=(4.3±4.3)×10(-3), and x'2=(0.08±0.18)×10(-3). We report Bayesian probability intervals in the x'2-y' plane and find that the significance of excluding the no-mixing hypothesis is equivalent to 6.1 Gaussian standard deviations, providing the second observation of D0-D¯0 mixing from a single experiment.