The analysis of color-superconducting two-flavor deconfined quark matter at moderate densities is extended to include a particular spin-1 Cooper pairing of those quarks which do not participate in the standard spin-0 diquark condensate. (i) The relativistic spin-1 gap delta(') implies spontaneous breakdown of rotation invariance manifested in the form of the quasifermion dispersion law. (ii) The critical temperature of the anisotropic component is approximately given by the relation T(')(c) approximately delta(')(T=0)/3. (iii) For massless fermions the gas of anisotropic Bogolyubov-Valatin quasiquarks becomes effectively gapless and two dimensional. Consequently, its specific heat depends quadratically on temperature. (iv) All collective Nambu-Goldstone excitations of the anisotropic phase have a linear dispersion law and the whole system remains a superfluid. (v) The system exhibits an electromagnetic Meissner effect.