The Jaguares recorded their first ever win over the Hurricanes to move to the top of the South African conference, handing their hosts a first home defeat by foreign opposition since 2015.
Agustin Creevy and Jeronomio De La Fuente crossed and the Argentines were awarded a penalty try when Jordie Barrett was sinbinned for a professional foul to give the visitors a 21-8 halftime lead.
Julian Montoya grabbed a fourth try after the break to ensure a victory that gave the Jaguares 32 points and moved them above the resting Sharks (29). The Bulls (28) play the Rebels in Melbourne later on Friday.
Vaea Fifita, Ngani Laumape and Kane Leaupepe scored tries for the home side, who remained second in the New Zealand conference on 40 points but were outplayed by a Jaguares team that constantly harried them and forced errors.