Network Function Virtualization (NFV) enables software implementations of middleboxes such as load balancing, traffic engineering and quality of service. These often rely on network measurement such as per-flow frequency estimation, bandwidth estimation, counting distinct elements and estimating the traffic entropy. Keeping up with the line speed is an active challenge for NFV measurement techniques, and library algorithms are simply too slow. Sampling is a natural technique to increase the measurement throughput, but it requires a certain amount of traffic before accuracy is guaranteed. In this work, we introduce a throughput acceleration method that preserves accuracy from the very first packet. This technique works with a variety of existing measurement algorithms (e.g., the ones mentioned above), and improves their throughput while guaranteeing their correctness throughout the entire measurement. Our work includes a rigors analysis, an extensive evaluation with real network traces, and a real DPDK enabled Open vSwitch implementation.