Semi-Dirac fermions are known to exist at the critical points of topological phase transitions requiring fine-tuning of the parameters. We show that robust semi-Dirac points can appear in a heterostructure consisting of superconducting Sr2IrO4 and a t2g electron system (t2g-ES) without fine-tuning. They are topologically stable in the presence of the symmetries of the model, metallic t2g-ES and a single active band in Sr2IrO4. If the t2g metal is coupled to two different layers of Sr2IrO4 (effectively a multiband superconductor) in a three-layer-structure the semi-Dirac points can split into two stable Dirac points with opposite chiralities. A similar transition can be achieved if the t2g-ES supports intrinsic triplet superconductivity. By considering Sr2RuO4 as an example of a t2g-ES we predict a rich topological phase diagram as a function of various parameters.