Dynamic Fault Trees (DFT) are widely adopted in industry to assess the dependability of safety-critical equipment. Since many systems are too large to be studied numerically, DFTs dependability is often analysed using Monte Carlo simulation. A bottleneck here is that many simulation samples are required in the case of rare events, e.g. in highly reliable systems where components fail seldomly. Rare Event Simulation (RES) provides techniques to reduce the number of samples in the case of rare events. We present a RES technique based on importance splitting, to study failures in highly reliable DFTs. Whereas RES usually requires meta-information from an expert, our method is fully automatic: by cleverly exploiting the fault tree structure we extract the so-called importance function. We handle DFTs with Markovian and non-Markovian failure and repair distributions (for which no numerical methods exist) and show the efficiency of our approach on several case studies.