This is how I see it.
General relativity relates the presence of energy-momentum to the curvature of space-time. From the curvature or space-time, we can compute time dilation and geodesics, which are phenomenon of study in GR.
You don't even need GR. Even in SR the flat 3-space must be embedded into a 4-dimensional Minowski space-time when we relate time with proper time and length with proper length.