There were very few chances in normal time, with Josip Drmic missing a glorious chance in the first half, and it looked destined for penalties until Di Maria's late winner.
Argentina will now face either Belgium or USA in the quarter-finals. Read how the action unfolded with our live text commentary below.
Argentina: Andujar, Orion, Campagnaro, Demichelis, Basanta, Biglia, Perez, Maxi Rodriguez, A.Fernandez, Alvarez, Palacio
Switzerland: Sommer, Burki, Senderos, Lang, Ziegler, Fernandes, Barnetta, Dzemaili, Stocker, Seferovic
Argentina and Switzerland are matched up for the Round of 16. Which team will prevail? Check the facts & stats here: pic.twitter.com/YE0xLGfxWg— SBOBETweets (@SBOBETweets) July 1, 2014