Due to limited resources on edge and different characteristics of deep neural network (DNN) models, it is a big challenge to optimize DNN inference performance in terms of energy consumption and end-to-end latency on edge devices. In addition to the dynamic voltage frequency scaling (DVFS) technique, the edge-cloud architecture provides a collaborative approach for efficient DNN inference. However, current edge-cloud collaborative inference methods have not optimized various compute resources on edge devices. Thus, we propose DVFO, a novel DVFS-enabled edge-cloud collaborative inference framework, which co-optimizes DVFS and offloading parameters via deep reinforcement learning (DRL). Specifically, DVFO automatically co-optimizes 1) the CPU, GPU and memory frequencies of edge devices, and 2) the feature maps to be offloaded to cloud servers. In addition, it leverages a thinking-while-moving concurrent mechanism to accelerate the DRL learning process, and a spatial-channel attention mechanism to extract DNN feature maps of secondary importance for workload offloading. This approach improves inference performance for different DNN models under various edge-cloud network conditions. Extensive evaluations using two datasets and six widely-deployed DNN models on three heterogeneous edge devices show that DVFO significantly reduces the energy consumption by 33% on average, compared to state-of-the-art schemes. Moreover, DVFO achieves up to 28.6%-59.1% end-to-end latency reduction, while maintaining accuracy within 1% loss on average.