Binary packing, encoding binary code prior to execution and decoding them at run time, is the most common obfuscation adopted by malware authors to camouflage malicious code. Especially, most packers recover the original code by going through a set of "written-then-executed" layers, which renders determining the end of the unpacking increasingly difficult. Many generic binary unpacking approaches have been proposed to extract packed binaries without the prior knowledge of packers. However, the high runtime overhead and lack of anti-analysis resistance have severely limited their adoptions. Over the past two decades, packed malware is always a veritable challenge to anti-malware landscape. This paper revisits the long-standing binary unpacking problem from a new angle: packers consistently obfuscate the standard use of API calls. Our in-depth study on an enormous variety of Windows malware packers at present leads to a common property: malware's Import Address Table (IAT), which acts as a lookup table for dynamically linked API calls, is typically erased by packers for further obfuscation; and then unpacking routine, like a custom dynamic loader, will reconstruct IAT before original code resumes execution. During a packed malware execution, if an API is invoked through looking up a rebuilt IAT, it indicates that the original payload has been restored. This insight motivates us to design an efficient unpacking approach, called BinUnpack. Compared to the previous methods that suffer from multiple "written-then-executed" unpacking layers, BinUnpack is free from tedious memory access monitoring, and therefore it introduces very small runtime overhead. To defeat a variety of ever-evolving evasion tricks, we design BinUnpack's API monitor module via a novel kernel-level DLL hijacking technique. We have evaluated BinUnpack's efficacy extensively with more than 238K packed malware and multiple Windows utilities. BinUnpack's success rate is significantly better than that of existing tools with several orders of magnitude performance boost. Our study demonstrates that BinUnpack can be applied to speeding up large-scale malware analysis.