Low-dimension carbon nanomaterials, such as carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs), are effective mechanical reinforcements in polymer composites. Epoxy matrix composites were fabricated by functionalizing CNT and GNP nanofillers using melamine and nondestructive ball milling. This noncovalent functionalization prevents agglomeration of nanofiller and produces direct CN bonds with the epoxy matrix. Compared to pristine CNTs and GNPs/epoxy nanocomposites, melamine-functionalized CNT (M-CNT)/epoxy and melamine-functionalized GNP (M-GNP)/epoxy nanocomposites exhibited considerably higher tensile strengths and fracture toughness (single edge notch bending, SENB). At 2 wt%, both M-CNT/epoxy and M-GNP/epoxy nanocomposites exhibited enhanced Young's modulus values (M-CNT: 64% and M-GNP: 71%) and ultimate tensile strengths (M- CNT: 22% and M-GNP: 23%). Fracture toughness increased by 95% with the 2 wt% M-CNT/epoxy and by 124% with the 2 wt% M-GNP/epoxy nanocomposite. The reinforcing effects of the two-dimensional M-GNPs were greater than those of the one-dimensional M-CNTs due to differences in pull-out mechanisms and bridging effects. Crack propagation in the nanocomposites, as it relates to fracture toughness, was also investigated.