This letter reports a measurement of the top quark mass, M_{top}, in data from p-pbar collisions at sqrt{s} = 1.96 TeV corresponding to 2.7 fb^{-1} of integrated luminosity at the Fermilab Tevatron using the CDF II detector. Events with the lepton+jets topology are selected. An unbinned likelihood is constructed based on the dependence of the lepton transverse momentum, P_T, on M_{top}. A maximum likelihood fit to the data yields a measured mass M_{top} = (176.9 +/- 8.0 stat +/- 2.7 syst) GeV/c^2. In this measurement, the contribution by the jet energy scale uncertainty to the systematic error is negligible. The result provides an important consistency test for other M_{top} measurements where explicit use of the jet energy is made for deriving the top quark mass.