The concept of intelligent reflecting surfaces (IRSs) is considered as a promising technology for increasing the efficiency of mobile wireless networks. This is achieved by employing a vast amount of low-cost individually adjustable passive reflect elements, that are able to apply changes to the reflected signal. To this end, the IRS makes the environment realtime controllable and can be adjusted to significantly increase the received signal quality at the users by passive beamsteering. However, the changes to the reflected signals have an effect on all users near the IRS, which makes it impossible to optimize the changes to positively influence every transmission, affected by the reflections. This results in some users not only experiencing better signal quality, but also an increase in received interference. To mitigate this negative side effect of the IRS, this paper utilizes the rate splitting (RS) technique, which enables the mitigation of interference within the network in such a way that it also mitigates the increased interference caused by the IRS. To investigate the effects on the overall power savings, that can be achieved by combining both techniques, we minimize the required transmit power, needed to satisfy per-user quality-of-service (QoS) constraints. Numerical results show the improved power savings, that can be gained by utilizing the IRS and the RS technique simultaneously. In fact, the concurrent use of both techniques yields power savings, which are beyond the cumulative power savings of using each technique separately.