We present high-precision V, B-V color-magnitude diagrams (CMDs) for the classic second-parameter globular clusters M3 and M13 from wide-field, deep CCD photometry. The data for the two clusters were obtained during the same photometric nights with the same instrument, allowing us to determine accurate relative ages. Based on a differential comparison of the CMDs using the {Delta}(B-V) method, an age difference of 1.7+/-0.7Gyr is obtained between these two clusters. We compare this result with our updated horizontal-branch (HB) population models, which confirm that the observed age difference can produce the difference in HB morphology between the clusters. This provides further evidence that age is the dominant second parameter that influences HB morphology.