The center kicked another penalty before Juan Martin Hernandez booted a drop goal and, despite Cusiter's late salvo, the unbeaten Pumas deserved to advance to their first World Cup semifinal.
Then, after Juan Martin Hernandez had crashed a drop goal against the post, the Pumas retook possession and prop Hasan was there at the bottom of a pile of bodies to ground.
However, Argentina hit back with a drop goal from Juan de la Cruz Fernandez Miranda and a string of five penalties from Federico Serra and Juan Martin Hernandez to lead 18-3 before Browne and the pack rumbled over.
South Africa flanker Juan Smith was sin-binned by New Zealand referee Steve Walsh for a high tackle on Hernandez in the 77th minute, causing a mass melee.