The dynamics of single DNA molecules conveyed in a viscoelastic fluid flow with an opposing electrophoretic force are investigated by fluorescence microscopy. For balanced hydrodynamic and electrophoretic forces, DNA is confined near the walls with a much smaller elongation than in bulk shear flows. Furthermore, we observe that DNA extension is characterized by intermittent fluctuations, the characteristic time scale of which depends on the flow velocity. A model based on Rouse dynamics explains the contraction of the molecule by the coupling of monomer motion in the transverse and longitudinal directions to the flow induced by transverse viscoelastic forces. Using simulations, we suggest that the occurrence of intermittent fluctuations is analogous to tumbling dynamics characterized by the cyclic spooling motion of end monomers about the molecule center of mass.