The ability to efficiently explore high-dimensional state spaces is essential for the practical success of deep Reinforcement Learning (RL). This paper introduces a new exploration technique called Random Latent Exploration (RLE), that combines the strengths of exploration bonuses and randomized value functions (two popular approaches for effective exploration in deep RL). RLE leverages the idea of perturbing rewards by adding structured random rewards to the original task rewards in certain (random) states of the environment, to encourage the agent to explore the environment during training. RLE is straightforward to implement and performs well in practice. To demonstrate the practical effectiveness of RLE, we evaluate it on the challenging Atari benchmark and show that RLE achieves competitive performance with exploration bonus methods on hard-to-explore tasks like Montezuma's Revenge, while simultaneously exhibiting higher overall scores across all the tasks than other approaches, including action-noise and randomized value function exploration.