Two red cards and a late yellow card proved to be Jaguares' undoing against Kings, with the South Africans producing a late comeback.
Kings managed to escape a humiliating defeat against Jaguares, who finished the match in Port Elizabeth with 12 men, with a late push earning a 29-22 win.
Tomas Lavanini was dismissed for a shoulder charge which annulled the try of Emiliano Boffelli, who subsequently left the match with an injury, and the Argentine side's woes increased when Ramiro Herrera was shown a red card for foul play before half-time.
Jaguares lost Tomas Lezana to the sin bin inside the final 10 minutes and Kings finally made their numerical advantage count to claim just their second win of the season.
"The two dismissals conditioned us for the rest of the game. We played as best we could," said Nicolas Sanchez, who kicked 17 points.
"We had to totally change our style, use the foot more and look for errors from them and score with penalties."
In a repeat of last year's final, Hurricanes came out on top against Highlanders, while Waratahs picked up a crucial victory over Chiefs.
Hurricanes 27-20 Highlanders
There was disappointment for the defending champions in Wellington as Ardie Savea, back in the Hurricanes side after being dropped for the victory over Queensland Reds for breaking a curfew, crossed twice to complete a double over Highlanders. Beauden Barrett kicked 12 points, meaning Lima Sopoaga's haul of two conversions, a try and a penalty was not enough for Jamie Joseph's team.
Waratahs 45-25 Chiefs
A big win for Waratahs consolidated top spot in the Australian conference ahead of the international break. Michael Hooper and Israel Folau touched down twice each in a six-try performance from the Sydney side, with Chiefs, just as they did in the win against Melbourne Rebels last week, proving sluggish in the second half.
Kings 29-22 Jaguares
Despite losing Lavanini and Herrera in the first half, the boot of Sanchez helped Jaguares build an unlikely 12-point lead against their South African opponents. There was to be no shock defeat, however, as tries from Dewald Human and Wandile Mjekevu inside the closing seven minutes steered Kings from the brink of humiliation to a much-needed victory.
THE KEY MOMENTS
Marty Banks' penalty tied things up at 20-20 at the Westpac Stadium, but there was to be a final twist in the tale with one minute of time remaining. Savea took the ball from the pack and darted across the line to hand Hurricanes the victory in dramatic fashion, with Barrett converting.
Despite being two men down, Facundo Isa pounced on a Kings error to help Jaguares move 22-10 up. However, a yellow card for Lezana in the 71st minute forced the Argentines to finish the match with 12 men, with the resultant penalty try immediately narrowing the gap. It gave Kings confidence to complete a late charge to avoid a seventh straight defeat.
"We came together, we worked together and we stayed in the match. There was great spirit in this team. It's very difficult to play with 13 players and more so with 12," said Nahuel Tetaz Chaparro after Jaguares' loss.
Waratahs victory puts them five points clear of second-placed Brumbies, who entertain Sunwolves on Saturday, in the Australian conference. Chiefs will be overtaken by Crusaders as leaders of the New Zealand conference if the latter win their game in hand against Blues.