We do NOT recommend doing so.
The skin around your eyes is much thinner and more delicate than the skin on the rest of your face. Facial moisturizer is designed for the skin on your face (which is thicker than the skin around the eyes) and will not absorb the same way around the eyes as it does on the face. Additionally, because the skin around your eyes is thinner, it is often drier than the skin on your face and therefore requires a bit more moisture.
We find it best to use eye cream under your eyes and facial moisturizer on the face.