We study, in the paradigm of open quantum systems, the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to the separation. The two-atom system is treated as an open system coupled with a bath of fluctuating massless scalar fields in the Minkowski vacuum, and the master equation that governs its evolution is derived. It has been found that, for accelerated atoms with a nonvanishing separation, entanglement sudden death is a general feature when the initial state is entangled, while for those in a separable initial state, entanglement sudden birth only happens for atoms with an appropriate interatomic separation and sufficiently small acceleration. Remarkably, accelerated atoms can get entangled in certain circumstances while the inertial ones in the Minkowski vacuum cannot. A comparison between the results of accelerated atoms and those of static ones in a thermal bath shows that uniformly accelerated atoms exhibit features distinct from those immersed in a thermal bath at the Unruh temperature in terms of entanglement dynamics.