Virtualization enables flexible application delivery and efficient resource consolidation, and is pervasively used to build various virtualized systems including public and private cloud computing systems. Many applications can benefit from computing on virtualized systems, including those that are time sensitive, but it is still challenging for existing virtualized systems to deliver application-desired timeliness. In particular, the lack of awareness between VM host- and guest-level schedulers presents a serious hurdle to achieving strong timeliness guarantees on virtualized systems. This paper presents RTVirt, a new solution to time-sensitive computing on virtualized systems through cross-layer scheduling. It allows the two levels of schedulers on a virtualized system to communicate key scheduling information and coordinate on the scheduling decisions. It enables optimal multiprocessor schedulers to support virtualized time-sensitive applications with strong timeliness guarantees and efficient resource utilization. RTVirt is prototyped on a widely used virtualization framework (Xen) and evaluated with diverse workloads. The results show that it can meet application deadlines (99%) or tail latency requirements (99.9th percentile) nearly perfectly; it can handle large numbers of applications and dynamic changes in their timeliness requirements; and it substantially outperforms the existing solutions in both timeliness and resource utilization.