The Chiefs came out on top of an incredible contest which saw the lead swing right until the end as they defeated the Jaguares 30-26.
Matias Moroni's spectacular try in the final five minutes looked to have clinched a superb opening win for the Jaguares on home soil in Super Rugby.
But the Chiefs had other ideas, dipping into the depth of the squad and overcoming an intense travel schedule to come up with the winning score through replacement Brad Weber to settle a quality contest.
Chiefs captain Sam Cane praised both his side and also the whole build-up to the fixture in Buenos Aires after the final whistle, but he may yet receive a call from the citing commissioner for a shoulder to the head of Jaguares prop Nahuel Tetaz Chaparro.
The crowd too played their part by creating a brilliant atmosphere, as Super Rugby made a successful debut in Argentina.
Aaron Cruden's early penalty got the scoring going for the Chiefs after the Jaguares strayed offside three minutes in.
Not for the first time in the contest though the Jaguares impressed in the scrum, winning a penalty for Nicolás Sánchez to knock over to level the scores.
Continuing their forward power the Jaguares went to the corner and used their driving maul to produce the game's first try, finished off from close range by the talismanic captain Agustín Creevy.
Not long after the Chiefs hit back thanks to the acrobatic finish of Sam McNicol, confirmed by the TMO that he grounded the ball before his feet fell out of bounds as he dove for the corner.
An error at the lineout by the Jaguares led to Damian McKenzie following his back-three partner over after the Chiefs put the ball through the hands to make it 8-13.
Again the Jaguares capitalised at the scrum, Sánchez knocking over the resulting penalty to close the gap.
Indiscipline cost the Chiefs dearly as they lost scrum-half Tawera Kerr-Barlow to a yellow card, Sánchez striking again to put the hosts ahead going into half-time at 14-13.
Seeking a response the Chiefs got one, thanks to a penalty from McKenzie to put the visitors back infront before they added their third try.
A smart change of direction from Anton Leinert-Brown freed up the space down the left wing for James Lowe to rush onto his pass for a score in the corner, stunning the home crowd into silence. McKenzie converted brilliantly from out on the touchline to make it 23-14.
Bad errors were costing the Jaguares when it came to both possession and field position as the hosts desperately tried to get something back on the scoreboard.
Two quick tries made up for all of those setbacks. First of all Martín Landajo did enough to ground the ball over the line after confirmation from the TMO, Sánchez converting superbly to close the gap to two points, before the Jaguares produced something special.
Starting well within their own 22 the Jaguares went on a 90-metre score, with Facundo Isa and Santiago González Iglesias combining brilliantly to release Matías Moroni for an sensational try as the crowd erupted.
But the Chiefs weren't done, keeping the ball alive superbly through Seta Tamanivalu to put Cruden down the touchline, before flinging the ball back infield for Weber to score with two minutes to go, McKenzie converting superbly to make it 26-30.
The Jaguares still had time to snatch the lead back again but a Chiefs penalty allowed the visitors to wind the clock down for a remarkable win in Buenos Aires, as Super Rugby debuted in Argentina in style.