The mechanism of electric field induced orientation-selective unzipping of carbon nanotubes into carbon nanoribbons upon oxidation is studied based on first-principles calculations. Under a controlled external electric field, the initial sparse O atoms are ordered to attack the transverse C-C bonds along a certain side of the carbon nanotube instead of a random site. In addition, the next O atoms tend to follow each initial O atom and stand on the adjacent transverse C-C bonds on this side, sequentially and automatically leading to a linear epoxy chain. Besides, it is noteworthy that an effortless O diffusion with reduced energy barriers allows the regular arrangement of an epoxy chain due to electron doping under a suitable electric field. An easier process for the unzipping of carbon nanotubes and longer graphene nanoribbons with smoother edges is expected under an external electric field.