Visible images from the Mars Reconnaissance Orbiter have revealed more than 200 new impact sites on Mars (almost all in dust-mantled regions) containing 1-50 m diameter craters, often in clusters. We count approximately 65,000 small-scale slope streaks within 2 to 3 km of one such cluster and categorize them into four morphologically distinct types. Here we show that these slope streaks (interpreted as dust avalanches) are triggered by the impact event but, surprisingly, are not due to seismic shaking; instead, the dust avalanches are due to airblasts created by the supersonic meteor(s) before impact. Sixteen of the new impact sites are associated with high areal densities of dust avalanches. The observed dust avalanche frequency suggests that impact-generated airblasts constitute a locally important and previously unrecognized process for inducing slope degradation on Mars.