A system and method for extracting headspace vapor is generally disclosed comprising pressurizing a vessel containing headspace vapor with a carrier gas and subsequently venting the sample mixture through an adsorbent trap and out a vent. A flow controller is employed to gradually increase the flow therethrough as the pressure drops as a result of the gradual depletion of headspace vapor in the vessel and, in certain embodiments, the flow controller maintains a constant flow rate. Due to the time saved, in some embodiments, multiple pressurization-venting cycles are implemented to maximize the amount of vapor extracted from the vial. Due to the constant flow rate, in certain embodiments, the pressure decay is monitored and compared to reference values in order to determine whether the sample vessel has a leak or other defect.