A system for erecting a drilling rig mast includes a substructure having an open area that is defined therein by two laterally spaced-apart substructure sides and a first mast section that is adapted to be positioned at least partially within the open area of the substructure after the first mast section has been removably connected to the substructure. The system further includes, among other things, a second mast section that is adapted to be removably connected to the first mast section the said first mast section has been removably connected to the substructure, and a mast connection apparatus that is adapted to removably connect the second mast section to the first mast section when an upper end of the first mast section is raised relative to a lower end of the second mast section.