Imperfect Channel State Information at the Transmitter (CSIT) is inevitable in modern wireless communication networks, and results in severe multi-user interference in multi-antenna Broadcast Channel (BC). While the capacity of the multi-antenna (Gaussian) BC with perfect CSIT is known and achieved by Dirty Paper Coding (DPC), the capacity and the capacity-achieving strategy of the multi-antenna BC with imperfect CSIT remain unknown. Conventional approaches therefore rely on applying communication strategies designed for perfect CSIT to the imperfect CSIT setting. In this work, we break this conventional routine and make two major contributions. First, we show that linearly precoded Rate-Splitting (RS), relying on the split of messages into common and private parts and linear precoding at the transmitter, and successive interference cancellation at the receivers, can achieve larger rate regions than DPC in multi-antenna BC with partial CSIT. Second, we propose a novel achievable scheme, denoted as Dirty Paper Coded Rate-Splitting (DPCRS), that relies on RS to split the user messages into common and private parts, and DPC to encode the private parts. We show that the rate region achieved by DPCRS in Multiple-Input Single-Output (MISO) BC with partial CSIT is enlarged beyond that of conventional DPC and that of linearly precoded RS. Gaining benefits from the capability of RS to partially decode the interference and partially treat interference as noise, DPCRS is less sensitive to CSIT inaccuracies, networks loads and user deployments compared with DPC and other existing transmission strategies. The proposed DPCRS acts as a new benchmark and the best-known achievable strategy for multi-antenna BC with partial CSIT.