Bidirectional cargo transport by kinesin and dynein is essential for cell viability and defects are linked to neurodegenerative diseases. The competition between motors is described as a tug-of-war, and computational modeling suggests that the load-dependent off-rate is the strongest determinant of which motor 'wins'. Optical tweezer experiments find that the load-dependent detachment sensitivity of transport kinesins is kinesin-3 > kinesin-2 > kinesin-1. However, when kinesin-dynein pairs were analyzed in vitro, all three kinesin families competed nearly equally well against dynein. One possible explanation is that vertical forces inherent to the large trapping beads enhance motor detachment. Because intracellular cargo range from ~30 nm to > 1000 nm, vertical forces in vivo are expected to range from near zero to larger than the horizontal forces of transport. To investigate detachment rates against loads oriented parallel to the microtubule, we created a DNA tensiometer comprising a DNA entropic spring that is attached to the microtubule on one end and a kinesin motor on the other. Surprisingly, kinesin dissociation rates at stall were slower than detachment rates during unloaded runs, a property termed a catch-bond. A plausible mechanism, supported by stochastic simulations, is that the strong-to-weak transition in the kinesin cycle is slowed with load. We also find evidence that the long run lengths of kinesin-3 (KIF1A) result from the concatenation of multiple short runs connected by diffusive episodes. The finding that kinesins form catch-bonds under horizontal loads necessitates a reevaluation of the role of cargo geometry in kinesin-dynein bidirectional transport.