DNA condensation in vivo usually requires proteins and/or multivalent salts. Here, we explore the in vitro compaction of DNA by cationic dendrimers having an intermediate size and charge. The dynamic assembly of DNA-dendrimer mesophases is discernible due to the laminar flow in a specially designed X-ray compatible microfluidic device. The setup ensures a nonequilibrium ascent of reactant concentration, and the resulting progression of DNA compaction was detected online using microfocused small-angle X-ray diffraction. The evolution of a DNA-dendrimer columnar square mesophase as a function of increasing dendrimer content is described. Additionally, in regions of maximum shear, an unexpected high-level perpendicular ordering of this phase is recorded. Furthermore, these assemblies are found to be in coexistence with a densely packed DNA-only mesophase in regions of excess DNA. The latter is reminiscent of dense packing found in bacteriophage and chromosomes, although surprisingly, it is not stabilized by direct dendrimer contact.