High-utility pattern mining is an important data mining task having wide applications. It consists of discovering patterns generating a high profit in databases. Recently, the task of high-utility sequential pattern mining has emerged to discover patterns generating a high profit in sequences of customer transactions. However, a well-known limitation of sequential patterns is that they do not provide a measure of the confidence or probability that they will be followed. This greatly hampers their usefulness for several real applications such as product recommendation. In this paper, we address this issue by extending the problem of sequential rule mining for utility mining. We propose a novel algorithm named HUSRM (High-Utility Sequential Rule Miner), which includes several optimizations to mine high-utility sequential rules efficiently. An extensive experimental study with four datasets shows that HUSRM is highly efficient and that its optimizations improve its execution time by up to 25 times and its memory usage by up to 50%.