Deep neural networks have produced tremendous advancements in super-resolution (SR) results. These improvements often come at the cost of inference latency, which is particularly important in low-resource devices. This paper therefore proposes a novel method to optimize the inference latency of SR models, called EHT-SR (Entropy-Based Hybrid Tiled SR), which leverages both accurate but slow DNN-based methods and a simple but fast bicubic interpolation for super-resolution. Particularly, we observe that a lightweight bicubic interpolation can still provide good image super-resolution quality for selected regions of the input image. An entropy-based heuristic, which we derive from a rigorous analysis of the bicubic interpolation, allows to select the best tiles in the input image that can be super-resolved using bicubic interpolation, while the remaining tiles are processed using a DNN-based SR method. This approach allows us to consistently speed-up the SR inference latency with only minimal degradation in image quality. Extensive evaluation results with different SR baselines and datasets show how our EHT-SR approach can speed-up inference by up to 27% and 39% on GPU and CPU platforms, respectively, without negatively impacting the quality of the super-resolved content.