A major challenge in reinforcement learning is to develop practical, sample-efficient algorithms for exploration in high-dimensional domains where generalization and function approximation is required. Low-Rank Markov Decision Processes---where transition probabilities admit a low-rank factorization based on an unknown feature embedding---offer a simple, yet expressive framework for RL with function approximation, yet existing algorithms either (1) are computationally intractable, or (2) require restrictive statistical assumptions such as latent variable structure or access to model-based function approximation. In this work, we propose the first provably sample-efficient algorithm for exploration in Low-Rank MDPs that is both computationally efficient and model-free, allowing for general function approximation while requiring no structural assumptions beyond a reachability condition that we show is substantially weaker than that assumed in prior work. Our algorithm, SpanRL, uses the notion of a barycentric spanner for the feature embedding as an efficiently computable basis for exploration, performing efficient spanner computation by interleaving representation learning and policy optimization subroutines. Our analysis---which is appealingly simple and modular---carefully combines several techniques, including a new approach to error-tolerant barycentric spanner computation, and a new analysis of a certain minimax representation learning objective found in prior work.