We applied both single-sample and isochron methods of cosmogenic-nuclide burial dating to determine the age of the sedimentary fill in Unaweep Canyon, western Colorado, USA. This stratigraphic sequence is of interest because it documents capture and diversion of the ancestral Gunnison River by the Colorado River during late Cenozoic incision of the Colorado Plateau. Seven 26Al–10Be burial ages from sedimentary infill penetrated by a borehole in central Unaweep Canyon, as well as a 26Al–10Be burial isochron age formed by multiple clasts and grain-size separates in a sample from the stratigraphically lower Gateway gravels, indicate that canyon blockage, initiation of lacustrine sediment accumulation, and presumed river capture, took place 1.41 ± 0.19 Ma. Lacustrine sedimentation ceased 1.34 ± 0.13 Ma.