It wasn't until front rower Alex Fidow crashed over in the 71st minute from close range after a scrum penalty that the Hurricanes looked like they could actually win the game, with some late heroics from Laumape, Vaea Fifita and Jamie Booth sealing an improbable victory.
The Jaguares were left to rue lapses in discipline which kept the Hurricanes in the match in the first half. Three penalties leading to nine points from the boot of Barrett – one struck through easily from 63m out – flatted the Hurricanes' efforts in the first half, as they struggled to provide much of a test with ball in hand.
It was a different story for the Jaguares, who looked dangerous when they had room to move and found success on the Hurricanes' edges, with Matias Moroni and Emiliano Boffelli asking plenty of questions of the visitors' defence.
Halfback Tomas Cubelli orchestrated the Jaguares attack nicely – distributing the ball well and putting a strong box kicking game to good use.
The hosts were rewarded for their early work when flanker Marcos Kremer was put through a gaping hole in the defence, storming across the line untouched.
Leading 10-9 at the break, the Jaguares went straight on the attack with the wind at their backs after halftime, again testing the Hurricanes line. Boffelli looked to have a try in the corner early in the period, however replays showed Barrett's cover defence was enough to force the Jaguares winger to drag his foot over the touch line before planting the ball.
It proved to be an important play in the swing of things, despite replacement hooker Agustin Creevy scoring from a lineout drive not long after.
Down 23-12 after another Barrett penalty, the Hurricanes looked on track to not only start with two losses, but to go without a try in their opening matches.
But simply having the ball in the Jaguares' half and being in a position to make the hosts defend finally came to something for the visitors; with Fidow crashing over before Booth sealed the win.
Hurricanes 26 (Alex Fidow, Jamie Booth tries; Jackson Garden-Bachop con, Fletcher Smith con, Jordie Barrett 4 pens)
Jaguares 23 (Marcos Kremer, Agustin Creevy tries; Domingo Miotti 2 cons, 3 pens)
HT: 9-10