The American Astronomical Society. All rights reserved.. The IceCube neutrino observatory has established the existence of a flux of high-energy astrophysical neutrinos, which is inconsistent with the expectation from atmospheric backgrounds at a significance greater than 5σ. This flux has been observed in analyses of both track events from muon neutrino interactions and cascade events from interactions of all neutrino flavors. Searches for astrophysical neutrino sources have focused on track events due to the significantly better angular resolution of track reconstructions. To date, no such sources have been confirmed. Here we present the first search for astrophysical neutrino sources using cascades interacting in IceCube with deposited energies as small as 1 TeV. No significant clustering was observed in a selection of 263 cascades collected from 2010 May to 2012 May. We show that compared to the classic approach using tracks, this statistically independent search offers improved sensitivity to sources in the southern sky, especially if the emission is spatially extended or follows a soft energy spectrum. This enhancement is due to the low background from atmospheric neutrinos forming cascade events and the additional veto of atmospheric neutrinos at declinations ≲-30.