Sediment flux in proglacial fluvial settings is primarily controlled by discharge, which usually varies predictably over a glacial–interglacial cycle. However, glaciers can flow against the topographic gradient to cross drainage divides, reshaping fluvial drainage networks and dramatically altering discharge. In turn, these variations in discharge will be recorded by proglacial stratigraphy. Glacial-drainage capture often occurs in alpine environments where ice caps straddle range divides, and more subtly where shallow drainage divides cross valley floors. We investigate discharge variations resulting from glacial-drainage capture over the past 40 k.y. for the adjacent Ashburton, Rangitata, and Rakaia basins in the Southern Alps, New Zealand. Although glacial-drainage capture has previously been inferred in the range, our numerical glacier model provides the first quantitative demonstration that this process drives larger variations in discharge for a longer duration than those that occur due to climate change alone. During the Last Glacial Maximum, the effective drainage area of the Ashburton catchment increased to 160% of the interglacial value with drainage capture, driving an increase in discharge exceeding that resulting from glacier recession. Glacial-drainage capture is distinct from traditional (base level–driven) drainage capture and is often unrecognized in proglacial deposits, complicating interpretation of the sedimentary record of climate change.