We present new measures of the evolving scaling relations between stellar mass, luminosity and rotational velocity for a morphologically-inclusive sample of 129 disk-like galaxies with z_AB<22.5 in the redshift range 0.2<z<1.3, based on spectra from DEIMOS on the Keck II telescope, multi-color HST ACS photometry, and ground-based Ks-band imaging. A unique feature of our survey is the extended spectroscopic integration times, leading to significant improvements in determining characteristic rotational velocities for each galaxy. Rotation curves are reliably traced to the radius where they begin to flatten for ~90% of our sample, and we model the HST-resolved bulge and disk components in order to accurately de-project our measured velocities, accounting for seeing and dispersion. We demonstrate the merit of these advances by recovering an intrinsic scatter on the stellar mass Tully-Fisher relation a factor of 2-3 less than in previous studies at intermediate redshift and comparable to that of locally-determined relations. With our increased precision, we find the relation is well-established by <z>~1, with no significant evolution to <z>~0.3, DeltaM_stellar ~ 0.04+/-0.07 dex. A clearer trend of evolution is seen in the B-band Tully-Fisher relation corresponding to a decline in luminosity of DeltaM_B ~ 0.85+/-0.28 magnitudes at fixed velocity over the same redshift range, reflecting the changes in star formation over this period. As an illustration of the opportunities possible when gas masses are available for a sample such as ours, we show how our dynamical and stellar mass data can be used to evaluate the likely contributions of baryons and dark matter to the assembly history of spiral galaxies.