Fault trees are a popular industrial technique for reliability modelling and analysis. Their extension with common reliability patterns, such as spare management, functional dependencies, and sequencing –- known as dynamic fault trees (DFTs) –- has an adverse effect on scalability, prohibiting the analysis of complex, industrial cases by, e.g., probabilistic model checkers. This paper presents a novel, fully automated reduction technique for DFTs. The key idea is to interpret DFTs as directed graphs and exploit graph rewriting to simplify them. We present a collection of rewrite rules, address their correctness, and give a simple heuristic to determine the order of rewriting. Experiments on a large set of benchmarks show substantial DFT simplifications, yielding state space reductions and timing gains of up to two orders of magnitude.