We present a new method to measure the top quark pair production cross section and the background rates with data corresponding to an integrated luminosity of 2.7  fb−1 from pp collisions at s√=1.96  TeV collected with the CDF II Detector. We select events with a single electron or muon candidate, missing transverse energy, and at least one b-tagged jet. We perform a simultaneous fit to a jet flavor discriminant across nine samples defined by the number of jets and b tags. An advantage of this approach is that many systematic uncertainties are measured in situ and inversely scale with integrated luminosity. We measure a top cross section of σtt=7.64±0.57(stat+syst)±0.45(luminosity)  pb.