1. A computer-implemented method for performing fast failovers, at least a portion of the method being performed by a computing device comprising at least one processor, the method comprising: identifying an application to fail over from a first computing system to a second computing system; identifying a first component of the application to fail over, the first component depending on a second component of the application and a third component of the application, the second component and third component being mutually independent; failing the application over from the first computing system to the second computing system by, based on a determination that the second component and third component are mutually independent: taking the first component offline on the first computing system before taking the second component offline on the first computing system; taking the second component offline on the first computing system after taking the first component offline on the first computing system; taking the third component offline on the first computing system while bringing the second component online on the second computing system; bringing the first component online on the second computing system after bringing the third component online on the second computing system.