Simultaneously supporting latency- and throughout-sensitive workloads in a shared environment is an increasingly more common challenge in big data clusters. Despite many advances, existing cluster schedulers force the same performance goal - fairness in most cases - on all jobs. Latency-sensitive jobs suffer, while throughput-sensitive ones thrive. Using prioritization does the opposite: it opens up a path for latency-sensitive jobs to dominate. In this paper, we tackle the challenges in supporting both short-term performance and long-term fairness simultaneously with high resource utilization by proposing Bounded Priority Fairness (BoPF). BoPF provides short-term resource guarantees to latency-sensitive jobs and maintains long-term fairness for throughput-sensitive jobs. BoPF is the first scheduler that can provide long-term fairness, burst guarantee, and Pareto efficiency in a strategyproof manner for multi-resource scheduling. Deployments and large-scale simulations show that BoPF closely approximates the performance of Strict Priority as well as the fairness characteristics of DRF. In deployments, BoPF speeds up latency-sensitive jobs by 5.38 times compared to DRF, while still maintaining long-term fairness. In the meantime, BoPF improves the average completion times of throughput-sensitive jobs by up to 3.05 times compared to Strict Priority.