Oseltamivir (Tamiflu) is currently the frontline antiviral drug employed to fight the flu virus in infected individuals by inhibiting neuraminidase, a flu protein responsible for the release of newly synthesized virions. However, oseltamivir resistance has become a critical problem due to rapid mutation of the flu virus. Unfortunately, how mutations actually confer drug resistance is not well understood. In this study, we employ molecular dynamics (MD) and steered molecular dynamics (SMD) simulations, as well as graphics processing unit (GPU)-accelerated electrostatic mapping, to uncover the mechanism behind point mutation induced oseltamivir-resistance in both H5N1 “avian” and H1N1pdm “swine” flu N1-subtype neuraminidases. The simulations reveal an electrostatic binding funnel that plays a key role in directing oseltamivir into and out of its binding site on N1 neuraminidase. The binding pathway for oseltamivir suggests how mutations disrupt drug binding and how new drugs may circumvent the resistance mechanisms.