Autonomous vehicles (AV) are expected to revolutionize transportation and improve road safety significantly. However, these benefits do not come without cost; AVs require large Deep-Learning (DL) models and powerful hardware platforms to operate reliably in real-time, requiring between several hundred watts to one kilowatt of power. This power consumption can dramatically reduce vehicles' driving range and affect emissions. To address this problem, we propose SAGE: a methodology for selectively offloading the key energy-consuming modules of DL architectures to the cloud to optimize edge energy usage while meeting real-time latency constraints. Furthermore, we leverage Head Network Distillation (HND) to introduce efficient bottlenecks within the DL architecture in order to minimize the network overhead costs of offloading with almost no degradation in the model's performance. We evaluate SAGE using an Nvidia Jetson TX2 and an industry-standard Nvidia Drive PX2 as the AV edge devices and demonstrate that our offloading strategy is practical for a wide range of DL models and internet connection bandwidths on 3G, 4G LTE, and WiFi technologies. Compared to edge-only computation, SAGE reduces energy consumption by an average of 36.13%, 47.07%, and 55.66% for an AV with one low-resolution camera, one high-resolution camera, and three high-resolution cameras, respectively. SAGE also reduces upload data size by up to 98.40% compared to direct camera offloading.